1997 CEMC Pascal Problems/Problem 5

Problem

If $60\%$ of a number of $42$ , what is $50\%$ of the same number?

$\text{ (A) }\ 25 \qquad\text{ (B) }\ 28 \qquad\text{ (C) }\ 30 \qquad\text{ (D) }\ 35 \qquad\text{ (E) }\ 40$

Let $x$ be the number. We then have:

$60\% \times x = 42$

$\frac{60}{100} \times x = \frac{6}{10} \times x = 42$

$x = 42 \times \frac{10}{6}$

$x = 70$

$50\%$ of $70$ is $50\% \times 70$ = $0.50 \times 70 = \boxed {\textbf {(D) } 35}$

~anabel.disher

Let $x$ be the number, like in solution 1. We then have:

$\frac{6}{10} \times x = 42$

However, since $50\% = \frac{5}{10}$ , we can multiply this by $\frac{5}{6}$ to get $50\%$ of the number:

$\frac{6}{10} \times \frac{5}{6} \times x = 42 \times {5}{6}$

The $6$ in the numerator and denominator of the fractions cancel out, leaving:

$\frac{5}{10} \times x = 50\% \times x = \boxed {\textbf {(D) } 35}$

~anabel.disher