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?

Answer 1

Answer: The cost of each sandwich (S) is $4 and the cost of each bottle of water (B) is $2.

Explanation:

10S + 6B = 52 (Equation 1) -- Ramon's purchase

1S + 3B = 10 (Equation 2) -- Wallace's purchase

To solve these equations, we can use a method called substitution. We'll solve Equation 2 for S and substitute it into Equation 1:

From Equation 2, we can isolate S:

1S = 10 - 3B

S = 10 - 3B

Substituting S into Equation 1:

10(10 - 3B) + 6B = 52

100 - 30B + 6B = 52

100 - 24B = 52

-24B = 52 - 100

-24B = -48

B = -48 / -24

B = 2

Now, substitute the value of B back into Equation 2 to find S:

S + 3(2) = 10

S + 6 = 10

S = 10 - 6

S = 4