Question

10. You have two jobs. You earn $8 for each hour x that you work as a restaurant host and $6 for each hour y that you work as a hair washer. Your earnings for the pay period are $144.

a. Write an equation in standard form that models your earnings.

b. Find the x- and y-intercepts.

c. You worked 10 hours as a hair washer. How many hours did you work as a host?

Answer 1

(these answers could be wrong but I did the best I could)

ANSWERS:

A) y = -4/3x +24
B) y intercept of (0,24)
C) total of 22 2/3 hrs

STEP BY STEP:

A)
We know that 6 is y and 8 is x. We also know that your earnings is a total is $144. To put this in an equation we have to add 6(y) and 8(x) to equal 144. This creates the following equation. ⇩

6y+ 8x = 144
put the equation in y= mx+b form or standard form. ⇩

6y + 8x = 144
(next, subtract 8x on both sides to put y alone)

6y + 8x = 144
- 8x = - 8x
6y = - 8x + 144
(next, divide each number by 6 to make 6y just y)

6y = - 8x + 144
/6 = /6 /6
y = -4/3x + 24⇩

B) Since the y intercept is b in the equation, the y intercept is (0,24)

C) make y the final answer. Substitute 10 for x and solve the equation. ⇩

Y = -4/3 (10) + 24
Y = -40/3 (or in mixed number -13 1/3) + 24
Y = -68/3 (or 22 2/3 )⇩

You worked a total of 22 2/3 hrs.

Answer 2

Explanation:

The equation in standard form is:

8x + 6y = 144

To find the y-intercept, isolate y.

8x + 6y = 144

Subtract 8x from both sides.

6y = -8x + 144

Divide both sides by 6.

y = -4/3x + 24

From this, we know (0, 24) is the y-intercept because b, which in this case, is the y value for the y-intercept.

To find the x-intercept, input y as 0.

0 = -4/3x + 24

Subtract 24 from both sides.

-24 = -4/3x

Multiply both sides by 3/-4.

18 = x

The x -intercept is (18, 0).

Input 10 for y because that's how many hours you worked as a hair washer.

8x + 6(10) = 144

Simplify.

8x + 60 = 144

Subtract both sides by 60.

8x = 84

Divide both sides by 8.

x = 10.5

You worked 10.5 hours as a host.