Brian O'Reilly earns twice as much each week as a tutor than he does pumping gas. His total weekly wages are $150 more than that of his younger sister. She earns one quarter as much as Brian does as a tutor. How much does Brian earn as a tutor?

let his wages from pumping gas be x

then his wages from tutoring is 2x
Brian's total wages = 3x

Sisters wages are 1/4 of Brian's tutor wages
= (1/4)(2x) = x/2

His wages from tutoring are 150 more than sister's wages
3x = x/2 + 150
6x = x + 300
5x = 300
x = 60

So he makes 2x or $120 as a tutor.

check: Brian's wages = 60 + 120 = 180
Sister's wages = (1/4) of 120 = 30
180 is 150 more than 30

i think its 37.50

this problem is killing me

To find out how much Brian earns as a tutor, let's break down the information given in the problem step by step.

1. Let's assume Brian earns x dollars per week as a tutor.

2. It is stated that Brian earns twice as much as a tutor as he does pumping gas. Therefore, Brian's weekly wages for pumping gas would be (1/2)x dollars. (Since he earns twice as much as a tutor, we divide x by 2).

3. The problem also states that Brian's total weekly wages are $150 more than that of his younger sister. Let's assume his sister earns y dollars per week.

4. According to the problem, Brian's younger sister earns one quarter as much as Brian does as a tutor. Therefore, her weekly earnings would be (1/4)x dollars.

5. Now, we can set up an equation to represent the information given in the problem. Brian's total weekly wages are the sum of his earnings as a tutor and pumping gas, which is x + (1/2)x. This can be written as (3/2)x. His younger sister's total weekly wages are y dollars.

6. As per the problem, Brian's total weekly wages are $150 more than his sister's. So, we can write the equation as follows: (3/2)x = y + $150.

To find the value of x, we need to substitute the value of y into the equation.

7. We know that Brian's sister earns (1/4)x dollars per week. Therefore, we can substitute y with (1/4)x in the equation: (3/2)x = (1/4)x + $150.

8. Let's solve the equation to find the value of x:

- Multiply each side of the equation by 4 to eliminate the fraction: 4 * (3/2)x = 4 * [(1/4)x + $150], which simplifies to 6x = 1x + $600.

- Subtract x from both sides: 6x - x = 1x + $600 - x. This simplifies to 5x = $600.

- Divide both sides by 5 to solve for x: (5x) / 5 = $600 / 5. This simplifies to x = $120.

Hence, Brian earns $120 as a tutor each week.