Casey orders 3 pizzas and 2 orders of breadsticks for a total of $29.50. Rachel orders 2 pizzas and 3 orders of breadsticks for a total of $23. How much would it cost to order 5 pizzas and 6 orders of breadsticks?

$54.50

Step-by-step explanation:

3 pizzas + 2 breadsticks = $29.50

2 pizzas + 3 breadsticks = $23  

5 pizzas + 6 breadsticks = $x

multipy first equation by 3 and second by -2

9 pizzas + 6 breadsticks = $88.50

-4 pizzas -6 breadsticks = $-46

add the equations up,  9-4 pizzas + 6-6 breadsticks = $88.50-46

5 pizzas = $42.50 , divide by 5 both sides

1 pizza = $8.50

Substitute the price of a pizza, 2 pizzas + 3 breadsticks = $23  

2*8.50 + 3breadstiks = $23

17 + 3 breadsticks = $23  subtract 17 from both sides so

3 breadsticks = $23 -$17 divide by 3

1 breadstick = 6/3= $2

$5*8.50 for pizzas + $6*2 for breadsticks = $54.50

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

sure i'm up for it

step-by-step explanation: