Question

A bag contains 80 more red marbles than black marbles. Ifthe ratio of red marbles 9 to 4, how many marbles are in the bag in total?

Answer 1

`let\text{ the number of black marbles be 'x'}`
`Then,\text{ the number of red }=\text{ x+80}`

The ratio of red marbles to black marbles is 9:4, this implies:

`(x+80)/(x)=(9)/(4)`

By cross-multiplying and solving for x, we have:

`\begin{gathered} 9x=4(x+80) \\ 9x=4x+320 \\ 9x-4x=320 \\ 5x=320 \\ x=(320)/(5) \\ x=64 \end{gathered}`

Thus, the number of red marbles is 64+80=144 and the number of black marbles is 64.

Hence, the total number of marbles in the bag is:

`144+64=208\text{ marbles}`