Question

7. Angela sold 4 boxes of pretzels and 6 bags of candy for a school fundraiser. Sheraised $108. Kevin raised $92 by selling 6 boxes of pretzels and 2 bags of candy. Howmuch was a box of pretzels worth? How much was a bag of candy worth?

Answer 1

Let P be the cost of a box of pretzels and C be the cost of a bag of candy.

The cost of 4 boxes of pretzels is 4P, and the cost of 6 bags of candy is 6C. Since Angela sold 4 boxes of pretzels and 6 bags of candy, raising $108, then:

`4P+6C=108`

Similarly, from Kevin's information we can conclude that:

`6P+2C=92`

These two equations lead to a 2x2 system of equations. To solve it, isolate C from the second equation:

`\begin{gathered} C=(92-6P)/(2) \\ \Rightarrow C=46-3P \end{gathered}`

Then, substitute the expression for C into the first equation:

`4P+6(46-3P)=108`

Solve this equation for P:

`\begin{gathered} \Rightarrow4P+276-18P=108 \\ \Rightarrow-14P+276=108 \\ \Rightarrow-14P=108-276 \\ \Rightarrow-14P=-168 \\ \Rightarrow P=(-168)/(-14) \\ \Rightarrow P=12 \end{gathered}`

Substitute P=12 into the expression for C to find its value:

`\begin{gathered} C=46-3(12) \\ =46-36 \\ =10 \end{gathered}`

Therefore, a box of pretzels is worth $12 and a bag of candy is worth $10.