Question

A baseball team is selling hats and pullovers for a fundraiser. The expression ax + 30y represents the cost of x hats and y pullovers. If each pullover costs $10 more than a hat, what is the value of the coefficient of x ?

Answer 1

a=20

Step-by-step explanation

Step 1

Let x represents the number of hats

a represents the cost of 1 hat

so, the cost of the hats is

`\cos t_(hats)=ax`

Also

Let y represents the number of pullovers

let 30 as the cost of 1 pullover

so, the cost of the pullovers is

`\text{Cost}_(pullovers)=30y`

so, the total cost is

`\begin{gathered} \text{total cost= Cost}_(hats)+Cost_(pullovers) \\ \text{total cost= ax+30y} \end{gathered}`

Step 2

If each pullover costs $10 more than a hat, in other words you have to add 10 to the cost of the hat to get the cost of the pullover

`\begin{gathered} \text{Cost}_(hat)+10=Cost_(pullover) \\ a+10=30 \\ \text{subtract 10 in both sides} \\ a+10-10=30-10 \\ a=20 \end{gathered}`

Hence, the cost of 1 hat ( a) is 20.

I hope this helps you