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. 
______(×+0.50)=25

GPT-4o mini · Answer

To fill in the missing place in the equation to compute the cost of each mechanical pencil, we need to first express the total cost of the mechanical pencils and erasers together.

Let $ x $ be the cost of one mechanical pencil in dollars. If Mr. Spears buys $ m $ bundles of mechanical pencils and $ n $ bundles of erasers, then:

The cost of the mechanical pencils would be $ m \cdot x $.
Since each bundle contains 10 erasers and each eraser costs $0.50, the cost for one bundle of erasers would be $ 10 \cdot 0.50 = 5 $ dollars.

Assuming he buys a certain number of bundles (let’s denote this by $ b $), then the total cost for $ b $ bundles of erasers is $ 5b $.

The equation for the total spending can then be expressed as: \[ (m \cdot x + 5b) = 25 \]

However, to simplify for just the pencils, let's say Mr. Spears buys $ y $ mechanical pencils. Then the equation becomes: \[ (y \cdot x + 5) = 25 \] where $ 5 $ is the total cost for the erasers (assuming he buys just 10 erasers, which would be one bundle).

We need to solve for $ y \cdot x $: \[ y \cdot x + 5 = 25 \] Subtract 5 from both sides: \[ y \cdot x = 20 \]

Thus, we can now fill in the original equation: \[ 20 + 0.50 = 25 \]

Therefore, the missing place in the equation is $ 20 $: \[ 20 \times + 0.50 = 25 \]

This means the cost of each mechanical pencil can be determined if we know how many pencils Mr. Spears wants to buy.