Question

You and a friend both work two different jobs. The system of linear equations represents the total earnings (in dollars) for x hours worked at the first job and y hours worked at the second job. Your friend earns twice as much as you.

4x+8y=64 You
8x + 16y - 128 Your Friend

a. One week, both of you work 4 hours at the first job. How many hours do you and your friend work at the second job?

b. Both of you work the same number of hours at the second job. Compare the numbers of hours you and your friend work at the first job.​

Answer 1

Explanation:

a. We can start by substituting y = 2x into the second equation to get an equation in terms of x only:

8x + 16y - 128 = 8x + 16(2x) - 128 = 0

Simplifying this equation, we get:

24x = 128

Solving for x, we get:

x = 128/24 = 32/6 = 16/3

So you and your friend work 16/3 hours (or approximately 5.33 hours) each at the second job.

b. If both of you work the same number of hours at the second job, then we can set x = y in the first equation and solve for y:

4x + 8y = 64

4x + 8x = 64

12x = 64

x = 64/12 = 16/3

So both you and your friend work 16/3 hours (or approximately 5.33 hours) at the second job.

To compare the number of hours worked at the first job, we can substitute x = 16/3 into the first equation to find:

4(16/3) + 8y = 64

64/3 + 8y = 64

8y = 64 - 64/3 = 128/3

y = 16/3

So your friend works 16/3 hours (or approximately 5.33 hours) at the first job, which is twice the amount of time you work at the first job.