Question

On Fridays, Jerry stops at Steak & Taco Shack before he goes home. This week

his order was 1 steak sandwich, 2 orders of cheese fries, and 2 taco salads. He was
charged $11.50 before tax. One week ago, his order was 2 steak sandwiches, 3
orders of cheese fries, and 1 taco salad, and he was charged $15.25. Two weeks ago
he ordered 1 steak sandwich, 4 orders of cheese fries, and 1 taco salad, and was
charged $13. How much is 1 steak sandwich? How much is 1 cheese fries? How
much is 1 taco salad?

Answer 1

Steak sandwich = x = 4

Cheese fries = y = 1.75

Taco salad = z = 2

Explanation:

Let :

Steak sandwich = x

Cheese fries = y

Taco salad = z

This week:

x + 2y + 2z = 11.50 - - - - (1)

Last week :

2x + 3y + z = 15.25 - - - (2)

Two weeks ago :

x + 4y + z = 13 - - - - - (3)

Taking (1) and (2)

x + 2y + 2z = 11.50 ___(1)

2x + 3y + z = 15.25 ___(2)

Multiply (1) by 2 and (2) by 1 and subtract

2x + 4y + 4z = 23

2x + 3y + z = 15.25

_______________

y + 3z = 7.75 - - - - (4)

Taking (2) and (3)

2x + 3y + z = 15.25 - - (2)

x + 4y + z = 13 - - - - - (3)

Multiply (2) by 1 and (3) by 2 and subtract

2x + 3y + z = 15.25

2x + 8y + 2z = 26

______________

-5y - z = - 10.75 - - - - - (5)

Lets solve (4) and (5)

y + 3z = 7.75 - - - - (4) - - - multiply by 5

-5y - z = - 10.75 - - - - - (5) - - - multiply by 1

Then add the result :

5y + 15z = 38.75

-5y - z = - 10.75

____________

14z = 28

z = 28 / 14

z = 2

To find y ; put z = 2 in (4)

y + 3z = 7.75

y + 3(2) = 7.75

y + 6 = 7.75

y = 7.75 - 6

y = 1.75

From equation 3 ;

x + 4y + z = 13 - - - - - (3)

x + 4(1.75) + 2 = 13

x + 7 + 2 = 13

x + 9 = 13

x = 13 - 9

x = 4

Hence,

Steak sandwich = x = 4

Cheese fries = y = 1.75

Taco salad = z = 2