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

**x = the number of hats sold**

y = the number of dollars of expense or income

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

**- Algebra House**