* He put most of the money in a money market account earning 5% simple interest. If a meal costs .75, what is the total after adding a 15% tip? How much is a 15% tip on a restaurant bill that totals .33? Ray has a handful of dimes and nickels valuing .05. If one brother averages 30 miles per hour in the car and the other averages 12 miles per hour on the bicycle, then it takes the brother on the bicycle 1 hour less than 3 times as long as the other in the car. 61: Jane has ,200 in the CD and ,200 in savings. 65: .76 67: .75 69: .66 71: He has 17 nickels and 22 dimes. 75: Mary has 7 one-dollar bills, 7 half-dollar coins, and 14 quarters.* Calculate the simple interest earned on a 2-year investment of * He put most of the money in a money market account earning 5% simple interest. If a meal costs $32.75, what is the total after adding a 15% tip? How much is a 15% tip on a restaurant bill that totals $33.33? Ray has a handful of dimes and nickels valuing $3.05. If one brother averages 30 miles per hour in the car and the other averages 12 miles per hour on the bicycle, then it takes the brother on the bicycle 1 hour less than 3 times as long as the other in the car. 61: Jane has $3,200 in the CD and $2,200 in savings. 65: $32.76 67: $42.75 69: $37.66 71: He has 17 nickels and 22 dimes. 75: Mary has 7 one-dollar bills, 7 half-dollar coins, and 14 quarters. Calculate the simple interest earned on a 2-year investment of $1,550 at a 8¾% annual interest rate. Calculate the simple interest earned on a 1-year investment of $500 at a 6% annual interest rate. For how many years must $10,000 be invested at an 8½% annual interest rate to yield $4,250 in simple interest? For how many years must $1,000 be invested at a 7.75% annual interest rate to yield $503.75 in simple interest? At what annual interest rate must $2,500 be invested for 3 years in order to yield $412.50 in simple interest? At what annual interest rate must $500 be invested for 2 years in order to yield $93.50 in simple interest? If the simple interest earned for 1 year was $47.25 and the annual rate was 6.3%, what was the principal? If the simple interest earned for 2 years was $369.60 and the annual rate was 5¼%, what was the principal? Joe invested last year’s $2,500 tax return in two different accounts. How long will it take the planes to be a distance of 1,478.75 miles apart? If Ted intends to catch up at a rate of 70 miles per hour, then how long will it take? Two brothers leave from the same location, one in a car and the other on a bicycle, to meet up at their grandmother’s house for dinner. Research ways to show that a repeating decimal is rational. 11: 8, 17 13: 22, 52 15: 4 17: 69, 70 19: 92, 93, 94 21: 15, 16 23: 118, 120 25: 18, 20 27: 33, 35 29: 17, 19, 21 31: 7, 9 33: 12 inches 35: Width: 5 feet; length: 8 feet 37: Width: 10 feet; length: 17 feet 39: 21 centimeters 41: 21 centimeters, 42 centimeters, 42 centimeters 43: 5 inches, 7 inches, 9 inches 45: 25 units 47: 15.9 centimeters 49: 15.7 inches 51: $271.25 53: 5 years 55: 5.5% 57: $750.00 59: Joe invested $2,050 in the money market account and $450 in the CD.* || * He put most of the money in a money market account earning 5% simple interest. If a meal costs $32.75, what is the total after adding a 15% tip? How much is a 15% tip on a restaurant bill that totals $33.33? Ray has a handful of dimes and nickels valuing $3.05. If one brother averages 30 miles per hour in the car and the other averages 12 miles per hour on the bicycle, then it takes the brother on the bicycle 1 hour less than 3 times as long as the other in the car. 61: Jane has $3,200 in the CD and $2,200 in savings. 65: $32.76 67: $42.75 69: $37.66 71: He has 17 nickels and 22 dimes. 75: Mary has 7 one-dollar bills, 7 half-dollar coins, and 14 quarters.* Calculate the simple interest earned on a 2-year investment of $1,550 at a 8¾% annual interest rate. Calculate the simple interest earned on a 1-year investment of $500 at a 6% annual interest rate. For how many years must $10,000 be invested at an 8½% annual interest rate to yield $4,250 in simple interest? For how many years must $1,000 be invested at a 7.75% annual interest rate to yield $503.75 in simple interest? At what annual interest rate must $2,500 be invested for 3 years in order to yield $412.50 in simple interest? At what annual interest rate must $500 be invested for 2 years in order to yield $93.50 in simple interest? If the simple interest earned for 1 year was $47.25 and the annual rate was 6.3%, what was the principal? If the simple interest earned for 2 years was $369.60 and the annual rate was 5¼%, what was the principal? Joe invested last year’s $2,500 tax return in two different accounts. How long will it take the planes to be a distance of 1,478.75 miles apart? If Ted intends to catch up at a rate of 70 miles per hour, then how long will it take? Two brothers leave from the same location, one in a car and the other on a bicycle, to meet up at their grandmother’s house for dinner. Research ways to show that a repeating decimal is rational. 11: 8, 17 13: 22, 52 15: 4 17: 69, 70 19: 92, 93, 94 21: 15, 16 23: 118, 120 25: 18, 20 27: 33, 35 29: 17, 19, 21 31: 7, 9 33: 12 inches 35: Width: 5 feet; length: 8 feet 37: Width: 10 feet; length: 17 feet 39: 21 centimeters 41: 21 centimeters, 42 centimeters, 42 centimeters 43: 5 inches, 7 inches, 9 inches 45: 25 units 47: 15.9 centimeters 49: 15.7 inches 51: $271.25 53: 5 years 55: 5.5% 57: $750.00 59: Joe invested $2,050 in the money market account and $450 in the CD. ,550 at a 8¾% annual interest rate. Calculate the simple interest earned on a 1-year investment of 0 at a 6% annual interest rate. For how many years must ,000 be invested at an 8½% annual interest rate to yield ,250 in simple interest? For how many years must * He put most of the money in a money market account earning 5% simple interest. If a meal costs $32.75, what is the total after adding a 15% tip? How much is a 15% tip on a restaurant bill that totals $33.33? Ray has a handful of dimes and nickels valuing $3.05. If one brother averages 30 miles per hour in the car and the other averages 12 miles per hour on the bicycle, then it takes the brother on the bicycle 1 hour less than 3 times as long as the other in the car. 61: Jane has $3,200 in the CD and $2,200 in savings. 65: $32.76 67: $42.75 69: $37.66 71: He has 17 nickels and 22 dimes. 75: Mary has 7 one-dollar bills, 7 half-dollar coins, and 14 quarters. Calculate the simple interest earned on a 2-year investment of $1,550 at a 8¾% annual interest rate. Calculate the simple interest earned on a 1-year investment of $500 at a 6% annual interest rate. For how many years must $10,000 be invested at an 8½% annual interest rate to yield $4,250 in simple interest? For how many years must $1,000 be invested at a 7.75% annual interest rate to yield $503.75 in simple interest? At what annual interest rate must $2,500 be invested for 3 years in order to yield $412.50 in simple interest? At what annual interest rate must $500 be invested for 2 years in order to yield $93.50 in simple interest? If the simple interest earned for 1 year was $47.25 and the annual rate was 6.3%, what was the principal? If the simple interest earned for 2 years was $369.60 and the annual rate was 5¼%, what was the principal? Joe invested last year’s $2,500 tax return in two different accounts. How long will it take the planes to be a distance of 1,478.75 miles apart? If Ted intends to catch up at a rate of 70 miles per hour, then how long will it take? Two brothers leave from the same location, one in a car and the other on a bicycle, to meet up at their grandmother’s house for dinner. Research ways to show that a repeating decimal is rational. 11: 8, 17 13: 22, 52 15: 4 17: 69, 70 19: 92, 93, 94 21: 15, 16 23: 118, 120 25: 18, 20 27: 33, 35 29: 17, 19, 21 31: 7, 9 33: 12 inches 35: Width: 5 feet; length: 8 feet 37: Width: 10 feet; length: 17 feet 39: 21 centimeters 41: 21 centimeters, 42 centimeters, 42 centimeters 43: 5 inches, 7 inches, 9 inches 45: 25 units 47: 15.9 centimeters 49: 15.7 inches 51: $271.25 53: 5 years 55: 5.5% 57: $750.00 59: Joe invested $2,050 in the money market account and $450 in the CD.* || * He put most of the money in a money market account earning 5% simple interest. If a meal costs $32.75, what is the total after adding a 15% tip? How much is a 15% tip on a restaurant bill that totals $33.33? Ray has a handful of dimes and nickels valuing $3.05. If one brother averages 30 miles per hour in the car and the other averages 12 miles per hour on the bicycle, then it takes the brother on the bicycle 1 hour less than 3 times as long as the other in the car. 61: Jane has $3,200 in the CD and $2,200 in savings. 65: $32.76 67: $42.75 69: $37.66 71: He has 17 nickels and 22 dimes. 75: Mary has 7 one-dollar bills, 7 half-dollar coins, and 14 quarters.* Calculate the simple interest earned on a 2-year investment of $1,550 at a 8¾% annual interest rate. Calculate the simple interest earned on a 1-year investment of $500 at a 6% annual interest rate. For how many years must $10,000 be invested at an 8½% annual interest rate to yield $4,250 in simple interest? For how many years must $1,000 be invested at a 7.75% annual interest rate to yield $503.75 in simple interest? At what annual interest rate must $2,500 be invested for 3 years in order to yield $412.50 in simple interest? At what annual interest rate must $500 be invested for 2 years in order to yield $93.50 in simple interest? If the simple interest earned for 1 year was $47.25 and the annual rate was 6.3%, what was the principal? If the simple interest earned for 2 years was $369.60 and the annual rate was 5¼%, what was the principal? Joe invested last year’s $2,500 tax return in two different accounts. How long will it take the planes to be a distance of 1,478.75 miles apart? If Ted intends to catch up at a rate of 70 miles per hour, then how long will it take? Two brothers leave from the same location, one in a car and the other on a bicycle, to meet up at their grandmother’s house for dinner. Research ways to show that a repeating decimal is rational. 11: 8, 17 13: 22, 52 15: 4 17: 69, 70 19: 92, 93, 94 21: 15, 16 23: 118, 120 25: 18, 20 27: 33, 35 29: 17, 19, 21 31: 7, 9 33: 12 inches 35: Width: 5 feet; length: 8 feet 37: Width: 10 feet; length: 17 feet 39: 21 centimeters 41: 21 centimeters, 42 centimeters, 42 centimeters 43: 5 inches, 7 inches, 9 inches 45: 25 units 47: 15.9 centimeters 49: 15.7 inches 51: $271.25 53: 5 years 55: 5.5% 57: $750.00 59: Joe invested $2,050 in the money market account and $450 in the CD. ,000 be invested at a 7.75% annual interest rate to yield 3.75 in simple interest? At what annual interest rate must ,500 be invested for 3 years in order to yield 2.50 in simple interest? At what annual interest rate must 0 be invested for 2 years in order to yield .50 in simple interest? If the simple interest earned for 1 year was .25 and the annual rate was 6.3%, what was the principal? If the simple interest earned for 2 years was 9.60 and the annual rate was 5¼%, what was the principal? Joe invested last year’s ,500 tax return in two different accounts. How long will it take the planes to be a distance of 1,478.75 miles apart? If Ted intends to catch up at a rate of 70 miles per hour, then how long will it take? Two brothers leave from the same location, one in a car and the other on a bicycle, to meet up at their grandmother’s house for dinner. Research ways to show that a repeating decimal is rational. 11: 8, 17 13: 22, 52 15: 4 17: 69, 70 19: 92, 93, 94 21: 15, 16 23: 118, 120 25: 18, 20 27: 33, 35 29: 17, 19, 21 31: 7, 9 33: 12 inches 35: Width: 5 feet; length: 8 feet 37: Width: 10 feet; length: 17 feet 39: 21 centimeters 41: 21 centimeters, 42 centimeters, 42 centimeters 43: 5 inches, 7 inches, 9 inches 45: 25 units 47: 15.9 centimeters 49: 15.7 inches 51: 1.25 53: 5 years 55: 5.5% 57: 0.00 59: Joe invested ,050 in the money market account and 0 in the CD.

If the perimeter is 102 inches, then find the measure of each side.

If the perimeter is 21 inches, find the measure of each side. A triangle has sides whose measures are consecutive integers.

Twice the sum of two consecutive odd integers is 32. If the perimeter is 26 feet, find the length and width. The width of a rectangle is 2 centimeters less than one-half its length. Each of the two equal legs of an isosceles triangle are twice the length of the base. The circumference of a circle measures 20 centimeters. If the simple interest earned from both accounts is $140 for the year, then how much does she have in each account? Marty put last year’s bonus of $2,400 into two accounts. She invests 3 times as much in the higher yielding account as she does in the lower yielding account. One bank offered 5.5% annual interest rate and the other 6¼%. One of the brothers, driving during the day, was able to average 70 miles per hour, and the other, driving at night, was able to average 53 miles per hour. Departing at the same time, they cycle toward each other. Jane and Holly live 51 miles apart and leave at the same time traveling toward each other to meet for lunch.

The difference between twice the larger of two consecutive odd integers and the smaller is 59. If the perimeter is 36 inches, find the length and width. The length of a rectangle is 2 feet less than twice its width. She has part of it in a CD at 3% annual interest and the rest in a savings account that earns 2% annual interest. Alice puts money into two accounts, one with 2% annual interest and another with 3% annual interest. If the total distance flown was 2,950 miles, then how long did the trip take? Two brothers drove the 2,793 miles from Los Angeles to New York. Discuss ideas for calculating taxes and tips mentally. Research historical methods for representing unknowns.

Solution: Let The key is to focus on the phrase “3 times the sum.” This prompts us to group the sum within parentheses and then multiply by 3.

Once an application is translated into an algebraic equation, solve it using the techniques you have learned. Jill has 3 fewer half-dollars than she has quarters. The average speeds for the planes are 450 miles per hour and 395 miles per hour. Bill leaves 1 hour earlier than Ted and travels at an average rate of 60 miles per hour. She has 1 fewer than three times as many tens as she does five-dollar bills. He has 3 more dimes than quarters and 5 more nickels than quarters. She has twice as many quarters than she does half-dollar coins and the same amount of half-dollar coins as one-dollar bills. He has 2 more than 3 times as many ones as he does five-dollar bills and 1 fewer ten- than five-dollar bills. If one car averages 55 miles per hour and the other averages 65 miles per hour, then how long will it take for them to separate a distance of 300 miles? Two planes leave the airport at the same time traveling in opposite directions.Step 3: Translate and set up an algebraic equation that models the problem. Step 5: Finally, answer the question in sentence form and make sure it makes sense (check it). For now, set up all of your equations using only one variable. These problems can sometimes be solved using some creative arithmetic, guessing, and checking. Example 4: The difference between two integers is 2. It is worth mentioning again that you can often find solutions to simple problems by guessing and checking. Solving in this manner is not a good practice and should be avoided. The larger integer is 6 less than twice the smaller. Solution: Use the relationship between the two integers in the second sentence, “The larger integer is 6 less than twice the smaller,” to identify the unknowns in terms of one variable. This is so because the numbers are chosen to simplify the process of solving, so that the algebraic steps are not too tedious. If the perimeter of a square is 48 inches, then find the length of each side. The length of a rectangle is 2 inches longer than its width. How much did he put in each account if the total interest for the year was 8.50? If the interest after 1 year was , how much did he invest in each account? Jane has her ,400 savings invested in two accounts. In an attempt to arrive before the storm, he increased his speed 400 miles per hour and flew for another 3 hours. Research and compare simple interest and compound interest. He invested the rest in a CD earning 8% simple interest. One account earns 4.25% simple interest and the other earns 8.5%. How long does it take each of them to make the trip? A commercial airline pilot flew at an average speed of 350 miles per hour before being informed that his destination airfield may be closed due to poor weather conditions. Step 1: Read the problem several times, identify the key words and phrases, and organize the given information. Step 2: Identify the variables by assigning a letter or expression to the unknown quantities. Eight times a number is decreased by three times the same number, giving a difference of 20.

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