Question

I have a bag with blue marbles and yellow marbles in it. At the moment, the ratio of blue marbles to yellow marbles is 8:5. If I remove 12 blue marbles and add 21 yellow marbles, the ratio will be 1:3. How many blue marbles were in the bag before I removed some

Answer 1

There were 15 blue marbles in the bag before removing some

Let B=blue marbles and Y= yellow marbles

The ratio of B to Y is

$\frac{B}{Y} =\frac{8}{5}$

If we remove 12 blue marbles and add 12 yellow marbles,

the ratio will be

$\frac{B-12}{Y+21} =\frac{1}{3}$

$3(B-12)=1(Y+21)$

$3B-36=Y+21$

$3(\frac{8}{5}Y)-36=Y+21$

$\frac{24}{5}Y-Y=21+36$

$\frac{19}{5}Y=57$

$Y=\frac{57*5}{19}$

$Y=15$

$B=\frac{8}{5} (15)\\B=24$

Hence, there were 15 blue marbles in the bag before removing some

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