A student can work at a job that pays $4 an hour for 25 hours to earn $100 or can work at a second job that pays $5 per hour for $20 to earn $100. If the student spends time at each job, find two other amounts of time at each job needed to earn $100.

30 Ha Gotee

To find the two other amounts of time at each job needed to earn $100, we can set up a system of equations.

Let's denote the number of hours worked at the first job as x and the number of hours worked at the second job as y.

Based on the given information, we can set up the following equations:

Equation 1: 4x + 5y = 100 (equation for the total earnings)

Equation 2: x + y = 25 (equation for the total number of hours worked)

We can solve this system of equations using substitution or elimination.

Method 1: Substitution
1. Solve Equation 2 for x: x = 25 - y.
2. Substitute the value of x in Equation 1: 4(25 - y) + 5y = 100.
3. Simplify and solve for y: 100 - 4y + 5y = 100. This gives y = 20.
4. Substitute y = 20 back into Equation 2: x + 20 = 25. This gives x = 5.

So, the student can work 5 hours at the first job and 20 hours at the second job to earn $100.

Method 2: Elimination
1. Multiply Equation 2 by 4: 4x + 4y = 100.
2. Subtract Equation 1 from the modified Equation 2 to eliminate x: (4x + 4y) - (4x + 5y) = 100 - 100. This simplifies to - y = 0, which means y = 0.
3. Substitute y = 0 back into Equation 2: x + 0 = 25. This gives x = 25.

So, the student can work 25 hours at the first job and 0 hours at the second job to earn $100.

Therefore, the two other amounts of time at each job needed to earn $100 are:
- 5 hours at the first job and 20 hours at the second job.
- 25 hours at the first job and 0 hours at the second job.