If 50% of the difference between two numbers equals 30% of their sum, then…
2017
If 50% of the difference between two numbers equals 30% of their sum, then what is the ratio between the numbers?
- A.
2 : 1
- B.
1 : 3
- C.
4 : 1
- D.
1 : 5
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Show answer & explanation
Correct answer: C
Solution:
Let the two numbers be x and y, with x ≥ y.
Given: 50% of the difference equals 30% of the sum.
Form the equation: 0.5(x - y) = 0.3(x + y)
Multiply both sides by 10 to eliminate decimals: 5(x - y) = 3(x + y)
Expand and simplify: 5x - 5y = 3x + 3y ⇒ 2x = 8y ⇒ x = 4y.
Therefore the ratio of the numbers is 4 : 1.
Quick check: Take numbers 4 and 1. 50% of difference = 0.5×3 = 1.5; 30% of sum = 0.3×5 = 1.5. They match.