ELIMINATION METHOD WORD PROBLEMS WORKSHEET

Problem 1 :

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?

Problem 2 :

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 $5.15. Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk?

Problem 3 :

The Frosty Ice-Cream Shop 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.

Problem 4 :

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. Which system of equations could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?

Problem 5 :

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?

Problem 6 :

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?

1. Answer

Let l and w be length and width respectively.

l = 3w 

2(l + w) = 85 

l - 3w = 0 ---> (1)

2l + 2w = 85 ---> (2)

2(1) - (2) :

w = 85/8

w = 10.625 cm

Substitute w = 10.625 into (1)

l - 3(10.625) = 0

l - 31.875 = 0

l = 31.875 cm

Therefore, the length and width are 31.875 cm and 10.625 cm.

2. Answer

Let t and m be the cost of taco and cost of milk.

t + m = 2.10 ---> (1)

2t + 3m = 5.15 ---> (2)

2(1) - (2) :

m = 0.95

Substitute m = 0.95 into (1)

t + 0.95 = 2.10

t = 2.10 - 0.95

t = 1.15

Therefore, the cost of taco and milk are 1.15 and 0.95.

3. Answer

Let s and b be the sundaes and banana.

2s + 3b = 156 ---> (1)

s = b + 8 

s - b = 8 ---> (2)

(1) + 3(2) :

s = 36

Substitute s = 36 into (2)

36 - b = 8

-b = 8 - 36

-b = -28

b = 28

4. Answer

Let f and g be the fudge and bubble gum.

5f + 3g = 5.70 ---> (1)

2f + 10g = 3.60 ---> (2)

2(1) - 5(2) :

g = 6.6/44

g = 0.15

Substitute g = 0.15 into (1)

5f + 3(0.15) = 5.70

5f + 0.45 = 5.70

5f = 5.25

f = 1.05

Therefore, cost of fudge and bubble gum are 1.05 and 0.15.

5. Answer

Let m and n be the math text book and novel.

m + n = 54 ---> (1)

m = 3n + 8

m - 3n = 8 ---> (2)

(1) - (2) :

n = 46/4

n = 11.5

Substitute n = 11.5 into (1)

m + 11.5 = 54

m = 54 - 11.5

m = 42.5

6. Answer

Let e and u be the Extreme electronics and Ultra electronics.

e - 2u = -220 ---> (1)

e - u = 175 ---> (2)

(1) - (2) :

u = 395

Substitute u = 395 into (2)

e - 395 = 175

e = 570