Question

aThe graph shows the number of bracelets and headbands sold by Alice and the profit earned. What number of bracelets must be sold to earn the same profit as earned by selling $12$ headbands?

• A. $20$
• B. $15$
• C. $25$
• D. $30$

Answer 1

The correct option is B $15$

Headband:

$x_1=4,y_1=25;x_2=6,y_2=37.5$
Unit rate $=\frac{\text{Rise}}{\text{Run}}=\frac{y_2-y_1}{x_2-x_1}=\frac{37.5-25}{6-4}=\frac{12.5}{2}$
Profit per headband $=\$12.52$
Profit from $12$ headbands $=\frac{12.5}{2}\times 12=12.5\times 6=\$75$
Bracelet:
$x_1=7,y_1=35;x_2=9,y_2=45$
Unit rate $=\frac{\text{Rise}}{\text{Run}}=\frac{y_2-y_1}{x_2-x_1}=\frac{45-35}{9-7}=\frac{10}{2}=5$
Profit per bracelet $=\$5$
Number of bracelets to be sold to earn $\$75=\frac{75}{5}=15$