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 cost $0.50

Question

Fill in the missing place in the equation to compute the cost of each mechanical pencil

Answer 1

Let's denote the cost of each mechanical pencil as $p$ and the number of mechanical pencils bought as $x$.

Mr. Spears' total budget is $25. The cost for erasers can be expressed as the number of bundles of erasers multiplied by the price per eraser. Since erasers come in bundles of 10 and cost $0.50 each, if he buys $y$ bundles, the cost for erasers can be computed as:

$$\text{Cost of erasers}=10\times 0.50\times y=5y$$

Now, if Mr. Spears spends part of his budget on erasers and the remaining part on mechanical pencils, we can express this as:

$$\text{Cost of mechanical pencils}=p\times x$$

Adding the two costs together gives us the equation:

$$p\times x+5y=25$$

To compute the cost of each mechanical pencil in terms of the other variables, you can rearrange the equation for $p$:

$$p\times x=25-5y$$

Dividing both sides by $x$ gives:

$$p=\frac{25-5y}{x}$$

Here, $p$ (the cost of each mechanical pencil) is expressed based on the number of eraser bundles $y$ and the total number of mechanical pencils $x$ purchased. You will need to know how many mechanical pencils and how many bundles of erasers are being bought to find the specific cost of each mechanical pencil.