Question

Your company takes out a loan for $750 and

makes a profit of $350 a week every week after

that. Write and solve an inequality to show how

many weeks it would take to make a profit of at

least $15,000 in your math notebook. Enter the

minimum number of weeks it would take to

make at least $15,000.

Answer 1

-750 + 350x
`\geq` 15000

and so it would take 45 weeks to make at least a 15000 dollar profit.

We know right away that the company's profit will be -750 dollars because they took out the loan. Every week then they will be gaining a positive 350 dollars of profit which we will add to that starting value of -750. This "350 per week" is a variable where x is the number of weeks. Due to us having to make at least 15000 dollar profit, we will use a greater than or equal to sign.

-750 + 350x
`\geq` 15000

Now to solve we have to isolate x

-750 + 350x
`\geq` 15000

350x
`\geq` 15750

x
`\geq` 45

45 weeks