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 \(b\)
\(8a=10b\)
⇒\(a=\frac{5}{4}b\)
⇒\(\frac{5}{4}b+b=90\)
⇒\(\frac{9}{4}b=90\)
⇒\(b=40\)
Number of red marbles in Jar 2 is \(9b=360\)
So there are 360 red marbles in Jar 2.
