# Ratio, Proportion and Percentages Puzzle – Challenge 24

This math puzzle is so challenging for students. Even the smartest one struggles to answer! Let's challenge your smart kid!

## Challenge:

The current ratio of girls to boys at a certain school is 2 to 7. If 10 additional girls were added to the school, the new ratio of girls to boys would be 3 to 8. How many girls currently attend the school?

**A-** 22

**B-** 32

**C-** 42

**D-** 56

**E-** 112

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

The correct answer is B.

Put x for the number of current girls and y for the number of current boys at the school. First, let’s set up our ratios.

\(\frac{x}{y} = \frac{2}{7}\) and \(\frac{x+10}{y }= \frac{3}{8 }\)

Use cross multiplication to write the equations.

\(7x = 2y\) and \(8 (x+10) = 3y ⇒ 8x + 80 = 3y\)

Now, we have a system of equations with two variables.

\(\begin{cases}7x-2y = 0\\ 8x-3y=-80\end{cases} \Rightarrow \begin{cases}8x-3y = -80\\ -16x+6y=160\end{cases}\)

From the system of equations above: \(x = 32\) and \(y = 112\)

32 girls are currently attending the school.

The Absolute Best Books to Ace AlgebraOriginal price was: $29.99.$19.99Current price is: $19.99.Original 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

- FREE 7th Grade SBAC Math Practice Test
- Ratio, Proportion and Percentages Puzzle – Challenge 28
- 6th Grade PACE Math Worksheets: FREE & Printable
- Full-Length 7th Grade PARCC Math Practice Test
- Top 10 8th Grade SBAC Math Practice Questions
- How to Add Mixed Numbers? (+FREE Worksheet!)
- How Is the CLEP College Algebra Test Scored?
- How to Use One Multiplication Fact to Complete Another One
- How to Analyze and Understand Rational Functions: A Comprehensive Guide
- How to Differentiate Trigonometric Reciprocals

## What people say about "Ratio, Proportion and Percentages Puzzle – Challenge 24 - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.