Question

Two identical jars are filled with equal numbers of marbles. The marbles are colored red or white. The ratio of red to white marbles is 7:1 in Jar 1 and

9:1 in Jar 2. If there are 90 white marbles all together, how many red marbles are in Jar 2?

Answer 1

Let
`a=`the number of white marbles in Jar 1
Let
`b=`the number of white marbles in Jar 2
Total number of white marbles is
`a+b=90`

Jar 1 has
`a` white marbles and
`7a` red marbles so
`8a` marbles total
Jar 2 has
`b` white marbles and
`9b` red marbles so
`10b` marbles total
Since both jars have equal amounts of marbles,
`8a=10b`

We have a system of equations:

`a+b=90`

`8a=10b`

The number of red marbles in Jar 2 is
`9b` so we solve for
`b`


`8a=10b`
⇒
`a=(5)/(4)b`
⇒
`(5)/(4)b+b=90`
⇒
`(9)/(4)b=90`
⇒
`b=40`
Number of red marbles in Jar 2 is
`9b=360`

So there are 360 red marbles in Jar 2.