Yesterday, Kate gave exactly fourteen haircuts and made $50.00. If she charged $5.00 for adults'
haircuts and $2.50 for children's haircuts, how
many children's haircuts did she give?
A) 5
B) 6
C) 7
D) 8

D) 8 Children’s Haircuts

Step-by-step explanation:

Let a represent the amount of adult haircuts and c represent the amount of child haircuts.

We know that she gave exactly 14 haircuts. So:

We also know that she made $50.00. Therefore, the price of each haircut times their respective amounts will total $50. So:

This is now a system of equations.

We can solve this using substitution. From the first equation, let’s subtract c from both sides:

Now, we can substitute this into the second equation for a. This yields:

Distribute:

Combine Like Terms:

Subtract 70 from both sides:

Divide both sides by -2.5:

Therefore, Kate gave 8 children’s haircuts.

This means that she gave adult haircuts.

So, our answer is D. She gave 8 children’s haircuts.

salary

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1