Mr. Spears was purchasing supplies for his math classroom. He had $25 to spend. Mechanical pencils and erasers come in bundles of 10. Each eraser costs $0.50. Fill in the missing place in the equation to compute the cost of each mechanical pencil.

Question

Mr. Spears was purchasing supplies for his math classroom. He had $25 to spend. Mechanical pencils and erasers come in bundles of 10. Each eraser costs $0.50. Fill in the missing place in the equation to compute the cost of each mechanical pencil.
? (x + 0.50)=25

GPT-4o mini · Answer

To find the cost of each mechanical pencil, let's break down the elements of the equation you provided:

The equation is formatted as: \[ ? (x + 0.50) = 25 \]

Here, $ x $ represents the cost of each mechanical pencil, and $ 0.50 $ is the cost of each eraser. Since erasers come in bundles of 10, the cost for a bundle of erasers is: \[ 10 \times 0.50 = 5 \]

Now we can express the total cost in terms of the number of mechanical pencils (let's say $ y $ is the number of mechanical pencils Mr. Spears buys). Hence, the cost of $ y $ mechanical pencils would be: \[ y \cdot x \]

The total cost equation becomes: \[ y \cdot x + 5 = 25 \]

This implies: \[ y \cdot x = 25 - 5 \] \[ y \cdot x = 20 \]

To find the value replacing the '?' in the equation $ ? (x + 0.50) = 25 $, we conclude that the '?' value represents the number of mechanical pencils purchased, which we had to express as $ y $ in our relationship. Thus, the final form could be represented as: \[ y (x + 0.50) = 25 \]

This indicates the number of bundles of mechanical pencils being multiplied by the total cost of mechanical pencils plus the cost of erasers equals the total amount Mr. Spears has to spend.

Summary

In the equation $ ? (x + 0.50) = 25 $, the '?' represents the total number of mechanical pencils bought $ y $.