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?

Short answer

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

Step-by-step solution

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.