Question

question 9 of 10
a caricature artist works 5 days a week, draws 18 portraits per day on
average, and charges $16 a portrait. if he lowers his price to $12 a portrait, by
how many portraits per day on average must he increase his production to
make the same amount of money per 5 - day workweek?

a. 12

b. 6

c. 24

d. 16

Explanation:

Step1: Calculate original weekly income

First, find the total number of portraits drawn in a week: \( 5 \text{ days} \times 18 \text{ portraits/day} = 90 \text{ portraits/week} \).
Then, calculate the original weekly income: \( 90 \text{ portraits} \times \$16/\text{portrait} = \$1440 \).

Step2: Find new daily portraits needed

Let \( x \) be the new number of portraits per day. The weekly number of portraits is \( 5x \).
The new price is \( \$12 \), so the weekly income equation is: \( 5x \times \$12 = \$1440 \).
Simplify: \( 60x = 1440 \) → \( x = \frac{1440}{60} = 24 \) portraits per day.

Step3: Calculate the increase per day

Original daily portraits: 18. New daily portraits: 24.
Increase: \( 24 - 18 = 6 \).

Answer:

B. 6