Question

SUPER URGENT!!

Joe and his brother are collecting money for a charity. Joe has already collected $170 and plans to earn at least $20 per week. His brother has $80, but plans to earn at least $40 per week. How many weeks until Joe's brother has more money than Joe? How much money will they each have at that point?

Please examples ALL OF THE STEPS YOU USED TO FIND THE ANSWER, or it's going to be useless. Thanks.

Answer 1

Let x be the number of weeks passed.

Denote by J(x) the money with Joe.

Denote by B(x) the money with his brother.

Denote by s(x) the money they raised together.

`J(x)=assets+money \: raised \\ J(x)=170 + 20x`

`B(x)=assets+money \: raised \\ B(x)=80+40x`

If we want Joe's brother to have more money at the x week, then B(x) has to be greater than J(x)

`B(x) > J(x) \\ 80 + 40x > 170 + 20x \\ 40x - 20x > 170 - 80 \\ 20x > 90 \\ x > (90)/(20) \\ x > 4.5 \: \: \: so \: \: \: x = 5`

We know that at the 5th week, Joe's brother will have raised more money than Joe, but how much money did they raise together by then?

`s(x) = B(x) + J(x) \\ s(5) = B(5) + J(5) \\ s(5) = 80 + 40(5) + 170 + 20(5) \\ s(5) = 80 + 200 + 170 + 100 \\ s(5) = 550 \: dollars \: raised`