Question

. 3. Two numbers are in the the natio 7:5. If 2 is sub . from each of them, the ratio becomes 3:2 Find the numbers.
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Answer 1

The numbers are 14 and 10.
Step-by-step explanation:
Ratio
A ratio indicates how many times one number contains another.
We can express ratio in three ways: colon form, fraction form and word form.
Going back to the problem above, ratios are given, we need to look for the two numbers that ratios represent.
Let us analyze the problem.
"Two numbers are in the ratio 7 : 5."
Let x be the number.
7x : 5x
"If 2 is subtracted from each of them, the ratio becomes 3 : 2."
7x-2 : 5x-2 = 3 : 2
Solution:
Let us express the ratios in fraction form so it is easier to solve.
7x-2/5x-2 = 3/2
Cross multiply.
3(5x-2) = 2(7x-2)
15x - 6 = 14x - 4
15x - 14x = 6 - 4
x = 2
Substitute the value of x.
7(2) : 5(2)
14 : 10
The numbers are 14 and 10.
Checking:
7x-2 : 5x-2 = 3 : 2
7(2)-2 : 5(2)-2 = 3 : 2
14-2 : 10-2 = 3 : 2
12 : 8 = 3 : 2
3 : 2 = 3 : 2 ✔