Question

6. Katie has a bag containing 265 pieces of candy. She takes 13 pieces for herself. Then she grabs 14 small sandwich bags for her friends and puts the same amount of candy in each bag. How many pieces of candy, x, could each friend get? A. Fill in the inequality symbol: Her candy and candy for her friends ___ Total Candy B. Write an inequality to represent the situation C. Solve for x D. Each friend could get __ pieces or

Answer 1

ANSWER and EXPLANATION

We have that Katie has a bag containing 265 pieces of candy.

She takes 13 pieces for herself and fits equal amounts into 14 sandwich bags.

A. The number of candy she and her friends will take must be less than or equal to the total number of candy, so:

`\text{Her candy and candy for her friends }\leq\text{ Total candy}`

B. x represents the pieces of candy that each friend receives.

It means that the sum of her candy and candy for her friends must be less than or equal to the total number of candy.

So:

`\begin{gathered} 13\text{ + 14 }\cdot\text{ x }\leq\text{ 265} \\ \Rightarrow\text{ 13 + 14x }\leq265 \end{gathered}`

C. To solve for x, we collect like terms and simplify:

`\begin{gathered} 14x\text{ }\leq265\text{ - 13} \\ 14x\text{ }\leq252 \\ x\text{ }\leq\text{ }(252)/(14) \\ x\text{ }\leq\text{ 18} \end{gathered}`

D. This means that each friend could get 18 pieces or less.