Question 1038468

The ratio of two number is 8:3. If 8 is added to the larger number and 7 is subtracted from the smaller number, the ratio of the numbers is 6:1. Find the smaller of the two original numbers.

I know the answer is 15 but i don't know how did it arrive to that answer. Please help me. Thank you.
<pre>Let multiplicative factor be x
Then larger and smaller numbers are: 8x and 3x, respectively
We then get: {{{(8x + 8)/(3x - 7) = 6/1}}}
6(3x - 7) = 1(8x + 8) -------- Cross-multiplying
18x - 42 = 8x + 8
18x - 8x = 8 + 42
10x = 50
x, or multiplicative factor = 5

{{{highlight_green(matrix(1,6, Smaller, number, "=", 3(5), or, 15))}}}