Question

Jake is selling items for his baseball fundraiser he earns $10 for each mug (x) he sells and $20 for each shirt (y) he sells. He want to earn at least $250 for his team.

1 ) write an inequality in standard form to represent the scenario
2) solve the above for y.
3)find and interpret the y-intercept

Answer 1

Explanation:

we are given that selling price of each mug(x) is $10

Selling price of each shirt(y) is $20.

Jake wants to earn atleast $250 for his team, So we can write

`(1)  10x+20y\geq 250`

(2) Now the above inequality can be solved for y as follows:

`10x+20y\geq 250\\\text{Add -10x on both the sides}\\10x+20y-10x\geq 250-10x\\20y\geq 250-10x\\\text{Divide both the sides by 20}\\y\geq 12.5-0.5x\\y\geq -0.5x+12.5`

(3)

By the observing the above equation that we just solved for y, we can say that It has an y-intercept of 12.5, and a negative slope of 0.5. Y-intercept of 12.5 means, jake must sell atleast 13 shirts to achieve the target.