Real-World Math problem

Question

Anthony Valencia sold his used mountain bike and his friend's accessories to a bicycle store for a total of $220. The store told Anthony that they paid him four times as much money for the bike as they did for his friend's accessories. Find how much money Anthony gets to keep, and how much he needs to pay back to his friend for the sale of his friend's accessories.

Answer 1

First, you must write an equation modeling this situation. The total amount Anthony was paid was $220, so we know that one side of the equation (let's say the right-hand side) equals 220. For the other side of the equation, we know that Anthony was paid for his bike and his friend's accessories. So, our equation looks like bike + accessories = 220. We also know that Anthony was paid a certain amount of money, that we can call x, for his friend's accessories. We also know that he was paid four times this unknown x amount for his bike. Therefore, we can say the total amount he was paid was x (accessories) + 4x (bike) = 220. Our equation is x+4x=220. Adding the x's together, we get 5x=220. Dividing both sides by 5, we get x=44. Therefore, we know that the amount Anthony got for his friend's accessories (and needs to give to his friend) was x, which was $44. The money Anthony gets to keep is the money from his bike which is 4x or 4*$44=$176.

Answer 2

Hello, Tylar,

Let's set A as the value of the accessories and B as the value of the bike.

We know that A + B = $220

We also found out from the store that they gave him four times the amount of the bike, B, for the accessories, A:

B = 4A

Take the first equation and use the definition of B provided by the second:

A + 4A = $220

5A = $220

A = $44

B = 4A, so B = 4*(44), or $176

The two amounts ($44 and $176) add to $220, and the value of the the bike was 4 times the value of the accessories. So I think we're good. [but I'd consider a management fee].

Bob