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.

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584