Systems of Equatins. Story Problems

Multiple Choice

A boy has seven more nickels than quarters. The total value of the coins is $4.90. Which system could be used to find out how many nickels and quarters he has?

Multiple Choice

Multiple Choice

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same.

Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

Multiple Choice

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315 2x + 4y = 450

• 3x + 2y = 450 2x + 4y = 315

• 2x + 2y = 315 3x + 4y = 450

Multiple Choice

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  It turns out that the doughnuts were more popular than the coffee.  On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 

• 10c + 5d = 14.25 5c + 10d = 16.50

• 10c + 5d = 16.50 5c + 10d = 14.25

• c + d = 10 5c + 10d = 16.50

• c + d = 5 5c + 10d = 16.50

Multiple Choice

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins and it came to $6.60.  Which system of equations could be used to find the exact number of dimes and nickels? 

• d + n = 6.60 .10d + .05n = 80

• d + n = 80 d + n = 6.60

• d + n = 80 .10d + .05n = 6.60

• d + n = 80 .05d + .10n = 6.60

Multiple Choice

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

• x + y = 1550

  y = 4x

• x + y = 1550

  y = x + 4

• y - x = 1550

  y = 4x

• y = 1550 + x

  y = x + 4

Multiple Choice

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38

  2s + 3c = 52

• 3s + 1c = 38

  3s + 2c = 52

• s + c = 38

  s + c = 52

• 3s + 3c = 38

  1s + 2c = 52

Multiple Choice

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables? 

• t: # of tacos m: # of glasses of milk

• t: Cost of each taco m: Cost of each glass of milk

• t: total cost m: # of food items

• t: Cost of each glass of milk m: Cost of each taco

Multiple Choice

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have?  Which system best represents the situation? 

• x + y = 1430 20x + 50y = 49

• x + y = 49 10x + 5y = 1430 

• x + y = 49 20x + 50y = 1430

• x + y = 49 x + y = 1430

Multiple Choice

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? 

• x + y = 6 14.80x + 17y = 91

• x + y = 91 14.80x + 17y = 6

• x + y = 6 14.80y + 17x = 91

• x + y = 91 14.80x+ 17y = 6

Multiple Choice

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530 3S + 4A = 1740

• S + A = 530 4S + 3A = 1740

• S + A = 1740 3S + 4A = 530

• S + A = 1740 4S + 3A = 530

Multiple Choice

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3 13.5x - 13y = 6

• x + y = 4 x - y = 6

• 4x + 6y = 13 3x + 7y = 13.5

• 4x - 6y = 13 3x - 7y = 13.5

Multiple Choice

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

• Sugar Cookies $5  Oatmeal Cookies $3

• Sugar Cookies $4 Oatmeal Cookies $8

• Sugar Cookies $2 Oatmeal Cookies $6

• Sugar Cookies $3 Oatmeal Cookies $6

Multiple Choice

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54 t = 3n + 8

• t + n = 54 n = 3t + 8

• t + n = 54 t = 3n - 8

• t + n = 8 t = 3n + 54