Molly placed two orders last week to Paneto's Pizzeria. In one order, she received 10 pizzas and 10 hero sandwiches for $137.50. In the other order, she received 15 pizzas and 8 hero sandwiches for $176.50. The price per item was not listed on the receipts. What is the price for one pizza, p, and one hero sandwich, h?

p= $9.50

h= $4.25

Step-by-step explanation:

First set up your equations:

10p+10h=137.50

15p+8h=176.50

Then choose one equation, and isolate either variable. I'm going to use the first equation and isolate p.

p+h=13.75  (divide by 10 on each side)

p=13.75-h

Now plug in the value for p into the second equation and evaluate

15(13.75-h)+8h=176.50

206.25-15h+8h=176.50

206.25-7h=176.50

29.75=7h

h=4.25

now plug in the value of h, (4.25) into any equation to find the value of p

10p+42.5=137.50

10p=95

p=9.5

h=4.25

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