Question

At a library fundraising event, Ramon paid $52 for 10 sandwiches and 6 bottles of water. Wallace paid $10 for 1 sandwich and 3 bottles of water. How much did each sandwich and bottle of water cost?

Learning Goal: I can use the substitution method to solve linear systems of equations.

Answer 1

sandwich = $4. bottle = $2

Explanation:

let's A = sandwich, B = bottle

elimination method:

10A + 6B = 52 (call this equation '1.' or just call it '1')

A + 3B = 10 (call this '2')

'2' X 2: 2A + 6B = 20 (call this '3')

'1' - '3':

8A + 0B = 32

A = 32/8 = 4

Sandwich costs $4.

go back to '2.'

3B = 10 - A = 10 - 4 = 6.

B = 6/3 = 2.

bottled water costs $2.

substitution method:

6B = 52 - 10A

3B = 26 - 5A.

'2.'

A + 3B = 10

A + (26 - 5A) = 10

-4A = -16

A = 4.

A + 3B = 10

3B = 10 - 4 = 6

B = 6/3 = 2.