Math question please help

Question

There are 4 times as many red pens as blue pens in a box. 415 red pens and 46 blue pens were removed from the box. As a result the number of blue pens became 3 times as many as red pens. How many blue pens were there in the beginning?

Answer 1

B = initial no. of blue pens; R = initial no. of red pens.

Also R = 4B

We know that after the pens are removed, the ratio of B to R = 3

So (B - 46)/(R - 415) = 3 Mult. both sides by (R - 415) to remove the fraction

B - 46 = 3(R - 415) → B - 46 = 3R - 1245 Substitute 4B for R

B - 46 = 12B - 1245 → 11B = 1199 → B = 109 so R must have be 4(109) = 436.

Check: Blue: 109 - 46 = 63; Red: 436 - 415 = 21 Ratio B:R = 3:1.