Question

Mike and Ken shared some stamps. \frac{1}{5} 5 1 ​ of Ken's stamps were \frac{1}{3} 3 1 ​ of Mike's stamps. If Mike gave Ken 24 stamps, Ken would have thrice as many stamps as Mike. Find the number of stamps each of them had in the beginning.

Answer 1

Answer:

Mike had 72 stamps

Ken had 120 stamps

Step-by-step explanation:

Given

$M \to Mike$

$K \to Ken$

$\frac{1}{5} * K = \frac{1}{3} * M$

$K + 24 = 3 * ( M - 24)$

Required

Find K and M

Make K the subject in: $K + 24 = 3 * ( M - 24)$

$K = 3 * ( M - 24) - 24$

Substitute $K = 3 * ( M - 24) - 24$ in $\frac{1}{5} * K = \frac{1}{3} * M$

$\frac{1}{5} * [3 * ( M - 24) - 24] = \frac{1}{3} * M$

Open brackets

$\frac{1}{5} * [3M - 72 - 24] = \frac{1}{3} * M$

$\frac{1}{5} * [3M -96] = \frac{1}{3} * M$

Multiply both sides by 15

$3* [3M -96] = 5 * M$

$9M -288 = 5M$

Collect like terms

$9M -5M= 288$

$4M= 288$

Divide both sides by 4

$M= 72$

Substitute $M= 72$ in $K = 3 * ( M - 24) - 24$

$K = 3 * (72 - 24) - 24$

$K = 3 * 48 - 24$

$K = 120$