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 = 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
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