A fashion designer makes and sell hats. The materials for each hats costs $5.50. The hats sell for $12.50 each. The designer spends $1400 an advertising. How many hat must the designer sell to break even

200 hats

Step-by-step explanation:

x = the number of hats sold

y = the number of dollars of expense or income

y = 12.5x {the income is $12.50 times the hats sold}

y = 5.5x + 1400 {the expense is $5.50 times the hats sold plus $1400 in advertising}

To break even means for the income to be equal to the expense.

12.5x = 5.5x + 1400 {substituted 12.5x, in for y, into bottom equation, setting income equal to expense}

7x = 1400 {subtracted 5.5x from each side}

x = 200 {divided each side by 7}

The designer must sell 200 hats to break even