SOLUTION: 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 origina

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.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Let the two numbers be n and d.
Their ratio is . The numerator here is obviously the larger of the two numbers.

The change: based on the description.

If all that makes sense for you, then you may be able to find a way to solve for n and d.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

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.

Let multiplicative factor be x
Then larger and smaller numbers are: 8x and 3x, respectively
We then get:
6(3x - 7) = 1(8x + 8) -------- Cross-multiplying
18x - 42 = 8x + 8
18x - 8x = 8 + 42
10x = 50
x, or multiplicative factor = 5

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