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It is always best to show examples with such types of questions.
Q: The ratio of two numbers is 3 to 4 and their sum is 84. What are their numbers?
A: We decide to use N for the numerator and D for denominator.
(a) N/D = 3/4 and (b) N + D = 84
We will cross multiply in (a), and then solve (b) for D and substitute into (a).
(a) N/D = 3/4 --> 4N = 3D (b) N + D = 84
4N = 3(84 - N) - substituted
4N = 252 - 3N - multiplied
7N = 252 - simplified
N = 36 - divided
Since N + D = 84, then D = 84 - 36 = 48
You now have N and D Solved
That in short is two statement or equality.
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Another form is:
Q: The sum of two numbers is 128 and their difference is 44. What are the numbers?
A: A little thought is choosing the variables is often helpful. Here we have two numbers. One is greater than the other, so we will use S to represent the small number and L to represent the large number. The equations are:
(a) L + S = 128 and (b) L - S = 44
We will solve the equations by using elimination.
(a) L + S = 128
(b) L - S = 44
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2L = 172 simplified
L = 82 solved
Thus,
S = 128 - 86 --> S = 42
Hope that helps.
Peace.
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