# 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

### The Absolute Best Book to Challenge Your Smart Student!

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.

The Best Books to Ace AlgebraOriginal price was: $29.99.$14.99Current price is: $14.99.Original price was: $29.99.$14.99Current price is: $14.99.Satisfied 1 StudentsOriginal price was: $24.99.$14.99Current price is: $14.99.Satisfied 92 StudentsOriginal price was: $24.99.$15.99Current price is: $15.99.Satisfied 125 Students

## Related to This Article

### More math articles

- The Ultimate 6th Grade GMAS Math Course (+FREE Worksheets)
- Finding the Area Between Two Rectangles
- The Ultimate 7th Grade SC Ready Math Course (+FREE Worksheets)
- HiSET Math Formulas
- 7th Grade STAAR Math FREE Sample Practice Questions
- Intelligent Math Puzzle – Challenge 88
- How to Identify Independent and Dependent Events?
- How to Solve the Ambiguous Case (SSA) in Trigonometry
- The Ultimate 6th Grade ILEARN Math Course (+FREE Worksheets)
- Top 10 Tips to Improve Your Low SAT Math Score

## What people say about "Algebra Puzzle – Challenge 57 - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.