Q49. - Algebra 1

Question

FIND THE ERROR Tim and Aisha are solving the following problem. Is either of them correct? Explain. Two years ago, 78 women were enrolled in a dance class, while 162 men were enrolled. This year 193 men enrolled, while the ratio of women to men did not change. How many women enrolled this year?

Step-by-Step Solution

Answer

Tim and Aisha both are incorrect. The correct answer will be $x=93$ or 93 women enrolled in this year.

Step 1. Understanding the concept of ratio.

A ratio is a number, which expresses one quantity as a fraction of the other.

For example, the ratio of 3 to 4 is $3:4$ or $\frac{3}{4}$.

Step 2. Choosing variables and finding ratios.

The ratio of women to men two years back was $\frac{78}{162}$ 

Let x be the number of women enrolled this year then the ratio of women to men This year will be $\frac{x}{193}$

Step 3. Equate the two ratios and solve.

 $\frac{78}{162}=\frac{x}{193}$

Cross multiplying we get,

 $$\begin{gathered} \frac{78}{162}=\frac{x}{193} \\ 78\times 193=162x \\ x=\frac{78\times 193}{162} \\ x=\mathrm{92.925...} \\ x\approx 93 \end{gathered}$$

Thus approximately 93 women enrolled this year.

Step 4. Verify the validity of Tim’s and Aisha’s work.

We are given,

 

Observe that Tim formed the equation incorrectly on the left-hand side.

Also, observe that Aisha formed the equation incorrectly on the right-hand side. 

Thus they both arrived at the wrong answer.