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 Algebra
Original 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
- 6th Grade Georgia Milestones Assessment System math Practice Test Questions
- 3rd Grade STAAR Math Practice Test Questions
- How to Complete a Table and Graph a Two-Variable Equation?
- How to Use Area Models to Find Equivalent Fractions
- Overview of the ALEKS Mathematics Test
- How to Find 3D Shapes Nets?
- Top 10 Tips to Overcome ATI TEAS 7 Math Anxiety
- Mastering Translations on the Coordinate Plane: A Step-by-Step
- Decoding the Dynamics: How to Understanding Input/Output Tables
- Jungle Bargains: A Guide How to Find the Original Price Using Sale Prices
What people say about "Ratio, Proportion and Percentages Puzzle – Challenge 24 - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.