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 $b$

$8a=10b$
⇒$a=\frac{5}{4}b$
⇒$\frac{5}{4}b+b=90$
⇒$\frac{9}{4}b=90$
⇒$b=40$
Number of red marbles in Jar 2 is $9b=360$

So there are 360 red marbles in Jar 2.