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

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x