SOLVING SYSTEMS OF EQUATIONS WORD PROBLEMS WORKSHEET

Problem 1 :

A large pizza at Palanzio's Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido's Pizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax?

Solution:

Let x represent the number of toppings and y represent the total money.

y = 0.9x + 6.80 ---> (1)

y = 0.65x + 7.30 ---> (2)

Solve (1) and (2),

0.9x + 6.80 = 0.65x + 7.30

0.9x - 0.65x = 7.30 - 6.80

0.25 = 0.5

x = 2

For Palanzio's Pizzeria and Guido's Pizza to cost the same, the number of toppings needed is 2.

Problem 2 :

Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. kitts sold of 110 CDs over the 2 weeks. Which system of equations can be used to find l, the number of CDs she sold last week, and t, the number of CDs she sold this week?

Solution:

Let t be the number of CDs sold this week

Let l be the number of CDs sold last week.

System of equations:

The total number of CDs she sold this week and last is 110.

l + t = 110

Last week she sold 6 more than 3 times the number of CDs she sold this week.

l = 3t + 6

Problem 3 :

The length of a rectangle is equal to triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 86 centimeters?

Solution:

Let L = length and W = width 

System of equations:

The length of a rectangle is equal to triple the width.

L = 3W

The rectangle has 2 lengths and 2 widths. so the perimeter is 

2(L + W) = 86

Problem 4 :

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. Determine t, the cost of a taco, and m, the cost of a small glass of milk?

Solution:

Let t be the taco and m be the milk.

System of equations:

The cost for a breakfast taco and a small glass of milk is $2.10.

t + m = 2.10

The cost for 2 tacos and 3 small glasses of milk is $5.15.

2t + 3m = 5.15

Problem 5 :

The Frosty Ice-Cream sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156. How many of each did they sell?

Solution:

Let b be the banana splits and s be the sundaes.

System of equations:

2s + 3b = 156

s = b + 8

Problem 6 :

Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. Determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?

Solution:

Let f be the fudge and g be the bubble gum.

System of equations:

Chase bought 5 pieces of fudge and 3 pieces of bubble gum for $5.70

5f + 3g = 5.70

Sara bought 2 pieces of fudge and 10 pieces of bubble gum for $3.60

2f + 10g = 3.60

Problem 7 :

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, m, 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?

Solution:

Let m be the math textbook and n be the novel.

System of equations:

Carla purchased a math textbook and a novel that cost a total of $54.

m + n = 54

Price of the math textbook is $8 more than 3 times the price of the novel

m = 3n + 8

Problem 8 :

The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics. The difference in price between the system at Extreme Electronics and Ultra Electronics is $175. Which system of linear equations can be used to determine the price of the system at each store?

Solution:

Let e be the price of an entertainment system at Extreme Electronics.

u be the price of an entertainment system at Ultra Electronics.

System of equations:

The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics.

e = 2u - 220

The difference in price between the system at Extreme Electronics and Ultra Electronics is $175.

e - u = 175

Problem 9 :

The perimeter of a rectangular wooden deck is 90 feet. The deck's length, l, is 5 feet less than 4 times its width, w. Which system of linear equations can be used to determine the dimensions, in feet, of the wooden deck?

Solution:

Let l be the length and w be the width.

System of equations:

The length of the rectangular wooden deck is 5 feet, less than 4 times the width.

l = 4w - 5

It is also given that the perimeter of the deck is 90 feet.

2l + 2w = 90

Problem 10 :

Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters. Then he solved the system by graphing. What is the solution?

Solution:

Let x be the number of nickels

y be the number of quarters.

System of equations:

Marcos had 15 coins in nickels and quarters.

x + y = 15

3 more quarters than nickels.

y = x + 3