Question

please answer this word problem for a medal:
The coin box of a vending machine contains 6 times as many quarters as dimes. If the total amount of money in quarters and dimes is $28.80, how many quarters and how many dimes are in the box?

Answer 1

please show work

Answer 2

6q = d
25q + 10d = 2880

Answer 3

please show work

Answer 4

should there be 2 answers? one for quarters, and one for dimes?

Answer 5

?

Answer 6

It should be 6d = q.

Subing we get,
25(6d) + 10d = 2880
Solve for d.

Answer 7

Then plug that value back into 6d = q

Answer 8

so the answer is...?

Answer 9

You tell me..

Answer 10

i don't understand what you wrote down

Answer 11

Do you know how to solve a system of equations? That's all we are doing here. \[\begin{matrix}q = 6d \\ 25q + 10d = 2880\end{matrix}\]The first equation represents the number of each coin. The second represents the money value of the coins. Quarts are 25 cents and dimes are 10 cents. As opposed to dealing with decimals, I multiplied these values by 100 and did the same to the total value.

First, step is to substitute 6d into the second equation for q. This yields. \[25(6d) + 10 d = 2880 \rightarrow 150d + 10 d = 2880 \rightarrow 160d = 2880 \rightarrow d = {2880 \over 160}\]
Second, we plug this value back into the first equation\[q = 6 \left(2880 \over 160 \right)\].