Question

Jacob is a construction worker who earns a yearly income given by the expression 2000x + 3000, where x is the number of hours he works each week. Carlos works with Jacob and earns a yearly income given by the expression 3800x – 40000. A manager predicts that if Carlos and Jacob each work 35 hours, they will earn the same amount of money.

PART A:The number of hours that makes the equation true is

Options: 24, 27, 29,31,34


PART B:Round your answer to the nearest whole number. The manager's prediction is

Options: equal to, less than, greater than


the actual number of hours that Carlos and Jacob need to work to earn the same amount of money.​

Answer 1

`x = 24`

24 is less than 35

Explanation:

Given

Jacob: 2000x + 3000

Carlos: 3800x - 40000

Solving (a):

To solve (a), we need to equate both expressions;

`3800x - 40000 = 2000x + 3000`

Collect Like Terms

`3800x - 2000x = 40000 + 3000`

`1800x = 43000`

Solve for x

`x = 43000/1800`

`x = 24` --- Approximated

Solving (b);

The manager's prediction is 35 hours.

And the actual hours is 24.

By comparison;

24 is less than 35