Question

Exercise #1: John mows yards for his father's landscaping business for $10 per hour and also works at a

bakery for $15 per hour. He can work at most 52 hours per week during the summer. He needs to make at least
$600 per week to cover his living expenses.
(a) If John works 14 hours mowing and 30 hours at (b) If x represents the hours John spends mowing
the bakery, does this satisfy all of the problem's and y represents the hours he spends at the
constraints?
bakery, write a system of inequalities that
describes this scenario.

Answer 1

The ordered pair not satisfy all of the constraints of the problem

see the explanation

Explanation:

Let

x ---> represents the hours John spends mowing

y ---> represents the hours John spends at the bakery

we know that

He can work at most 52 hours per week during the summer

The word "at most" means "less than or equal to"

so

`x+y\leq 52` ----> inequality A

He needs to make at least $600 per week to cover his living expenses.

The word "at least" means "greater than or equal to"

so

`10x+15y\geq 600` ----> inequality B

If John works 14 hours mowing and 30 hours at bakery

substitute the value of x and y in both inequalities

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

we have the ordered pair (14,30)

Verify inequality A

`14+30\leq 52`

`44\leq 52` ---> is true

so

The ordered pair satisfy the inequality A

Verify inequality B

`10(14)+15(30)\geq 600`

`590\geq 600` ----> is not true

so

The ordered pair not satisfy the inequality B

therefore

The ordered pair is not a solution of the system of inequalities

The ordered pair not satisfy all of the constraints of the problem