# Algebra Puzzle – Challenge 57

This mathematical puzzle requires some kind of math to solve. Let's challenge your brain with a great math challenge!

## Challenge:

The sum of three positive integers is 4000. The ratio of the first number to the second number is $$\frac{2}{3}$$ and the ratio of the first number to the third number is $$\frac{6}{5}$$. What is the third number?

A- 800

B- 1000

C- 1200

D- 1600

E- 2000

$11.99 Satisfied 123 Students The correct answer is B. Let X, Y and Z represent the three numbers. So, X + Y + Z = 4000 and $$X = \frac{2}{3} Y → Y = \frac{3}{2}X$$ $$X = \frac{6}{5} Z → Z = \frac{5}{6}X$$ Replace the values of Y and Z in the first equations with their values in the second and third equations: $$X + \frac{3}{2}X + \frac{5}{6}X = 4000 →X = 1200$$ $$Y = \frac{3}{2}X → Y = \frac{3}{2} (1200) = 1800$$ $$Z = \frac{5}{6}X → Z = \frac{5}{6}(1200) = 1000$$ The third number, Z, is 1000. ### More math articles ### What people say about "Algebra Puzzle - Challenge 57"? No one replied yet. X 30% OFF Limited time only! Save Over 30% SAVE$5

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