Question

The x-intercept shows that you can buy short-sleeve shirts and long-sleeve shirts. The y-intercept shows that you can buy long-sleeve shirts and short-sleeve shirts.

Answer 1

Question:

You are ordering short-sleeve shirts (x) for $10 and long-sleeve shirts (y) for $15. Your budget is $300. Write the equation and find the intercepts.

Interpret their meaning.

Answer:

The x-intercept shows that you can buy 30 short-sleeve shirts and 0 long-sleeve shirts.

The y-intercept shows that you can buy 20 long-sleeve shirts and 0 short-sleeve shirts.

Explanation:

Given

$10 per short sleeve

$15 per long sleeve

Budget = $300

The above can be represented as:

Total Cost of Short Sleeve + Total Cost of Long Sleeve = Budget

i.e.

`10 * x + 15 * y =300`

`10x + 15y =300`

To solve for the y intercept, we set x to 0

`10 * 0 + 15y =300`

`15y =300`

Divide through by 15

`y = 20`

This implies that, you can buy 0 short sleeves and 20 long sleeves

To solve for the x intercept, we set y to 0

`10x + 15 * 0 = 300`

`10x = 300`

Divide through by 10

`x = 30`

This implies that, you can buy 0 long sleeves and 30 short sleeves