Question

Margo spends a quarter of her paycheck on a new dress, One-eighthof her paycheck on shoes, and $24 on a birthday present. If she spent $60 altogether, how much was Margo’s paycheck?
$96
$160
$216
$504

Answer 1

Let \( x \) represent Margo's paycheck. According to the problem, she spends:

- A quarter of her paycheck on a dress: \( \frac{1}{4}x \)
- One-eighth of her paycheck on shoes: \( \frac{1}{8}x \)
- $24 on a birthday present

The total amount she spent is given as $60. Therefore, we can set up the equation:

\[
\frac{1}{4}x + \frac{1}{8}x + 24 = 60
\]

To simplify this equation, we first want to combine the fractional parts. We can find a common denominator for \( \frac{1}{4} \) and \( \frac{1}{8} \), which is 8. We can rewrite \( \frac{1}{4} \) as \( \frac{2}{8} \):

\[
\frac{2}{8}x + \frac{1}{8}x + 24 = 60
\]

Now we can combine the fractions:

\[
\frac{2}{8}x + \frac{1}{8}x = \frac{3}{8}x
\]

So, the equation becomes:

\[
\frac{3}{8}x + 24 = 60
\]

Next, we subtract 24 from both sides:

\[
\frac{3}{8}x = 60 - 24
\]
\[
\frac{3}{8}x = 36
\]

To solve for \( x \), multiply both sides by the reciprocal of \( \frac{3}{8} \), which is \( \frac{8}{3} \):

\[
x = 36 \cdot \frac{8}{3}
\]

Calculating this gives:

\[
x = 36 \cdot \frac{8}{3} = 12 \cdot 8 = 96
\]

Thus, Margo's paycheck is:

\[
\boxed{96}
\]