Question

Suppose you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an
hour and babysitting pays $5 an hour. You need to earn at least $60 a week.
a. Write a linear equation.

Answer 1

Answer:

The system of inequalities is

$x+y\leq 15$

$3x+5y\geq 60$

The graph in the attached figure

Step-by-step explanation:

The correct question is

Write a system of inequalities

Let

x ----> the number of hours worked mowing lawns

y ----> the number of hours worked as a babysitter

we know that

You can spend no more than 15 hours a week at your two jobs

The word "no more" means "less than or equal to"

so

$x+y\leq 15$ ----> inequality A

You need to earn at least $60 a week

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

so

$3x+5y\geq 60$ ----> inequality B

Solve the system of inequalities by graphing

The solution is the triangular shaded area

see the attached figure

Answer 2

The situation can be represented by a system of linear inequalities.

The system of linear inequalities that represent the situation are;

• 3·x + 5·y ≥ 60

• x + y ≤ 15

Reasons:

Number of hours available each week = 15 hours

The amount made from mowing lawns = $3/hour

The amount made from babysitting = $5/hour

Amount needed per week = $60

Required:

The equation representing the word problem.

Solution:

Let x represent the time spent mowing lawns , and let y represent the time

spent babysitting, we have the following linear inequalities;

3·x + 5·y ≥ 60

x + y ≤ 15

Which gives;

x ≤ 15 - y

3 × (15 - y) + 5·y ≥ 60

45 - 3·y + 5·y ≥ 60

2·y ≥ 60 - 45 = 15

y ≥ 7.5

x ≤ 7.5

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