Question

Chandler and Gabe went to the candy store. Chandler bought 6 pieces of fudge and 4 jawbreakers for a total of $5.30. Gabe bought 3 pieces of fudge and 10 jawbreakers for a total of $4.25. How much did each type of candy cost?

Answer 1

The cost of 1 piece of fudge, f = $0.75

The cost of 1 piece of jawbreaker, j = $0.2

Step-by-step explanation:

Let the cost of 1 piece of fudge = f

Let the cost of 1 piece of jawbreaker = j

Chandler bought 6 pieces of fudge and 4 jawbreakers for a total of $5.30.

`6f+4j=5.30`

Gabe bought 3 pieces of fudge and 10 jawbreakers for a total of $4.25

`3f+10j=4.25`

Next, solve the two equations simultaneously:

`\begin{gathered} 6f+4j=5.30\ldots(1) \\ 3f+10j=4.25\ldots(2) \\ \text{Multiply (1) by 10 and (2) by 4.} \\ 60f+40j=53 \\ 12f+40j=17 \end{gathered}`

Subtract:

`\begin{gathered} 48f=36 \\ f=(36)/(48) \\ f=0.75 \end{gathered}`

Substitute f to solve for j:

`\begin{gathered} 6f+4j=5.30\ldots(1) \\ 6(0.75)+4j=5.30 \\ 4j=5.30-6(0.75) \\ 4j=5.30-4.5 \\ 4j=0.8 \\ j=(0.8)/(4) \\ j=0.2 \end{gathered}`

We conclude that:

• The cost of 1 piece of fudge, f = $0.75

,

• The cost of 1 piece of jawbreaker, j = $0.2