Question

the two boys enter a lawn mowing business for the summer. they bought a lawn mower for 425 and plan to charge 25.00 an hour. A. how many hours did the boys work if their profit was more than 4,000. write and inequality. B. how many hours did the boys work if their profit was between 2,300 and 2,900write an inequality.

Answer 1

Given:

a.) They bought a lawnmower for 425 and plan to charge 25.00 an hour.

Question 1: How many hours did the boys work if their profit was more than 4,000.

`\text{ No. of hours the boys worked }>\text{ }\frac{4,000\text{ + cost of lawnmower}}{\text{ charge for doing the job}}`
`\text{ No. of hours the boys worked }>\text{ }\frac{4,000\text{ + 4}25}{\text{ 2}5}`

Let,

x = the number of hours the boys worked.

`\text{ x }>\text{ }\frac{4,425}{\text{ 2}5}`
`\text{ x }>\text{ 177 hours}`

Therefore, for the boys' profit to be more than 4,000, they must work for more than 177 hours.

Question 2: How many hours did the boys work if their profit was between 2,300 and 2,900.

For a profit of more than 2,300:

`\text{ No. of hours the boys worked }>\text{ }\frac{2,300\text{ + cost of lawnmower}}{\text{ charge for doing the job}}`
`\text{ x }>\text{ }\frac{2,300\text{ + 425}}{\text{ 2}5}`
`\text{ x }>\text{ }\frac{2,725}{\text{ 2}5}`
`\text{ x }>\text{ }109`

For a profit of less than 2,900:

`\text{ No. of hours the boys worked }<\text{ }\frac{2,900\text{ + cost of lawnmower}}{\text{ charge for doing the job}}`
`\text{x }<\text{ }\frac{2,900\text{ + 4}25}{\text{ 2}5}`
`\text{x }<\text{ }\frac{3,325}{\text{ 2}5}`
`\text{x }<\text{ }133`

Therefore, for a profit between 2,300 and 2,900, the inequality of how many hours must the boys work is:

`\text{ 109 }<\text{ x }<\text{ 133}`