Please help w math!!!!?

If they'd sold 38 of the cheap ones they would have only sold them for 342 dollars. But they got 73.50 more than that. For each small pizza you replace with a large one, that adds 3.50 to the total. How many 3.50's make 73.50? 21 of them. 73.50/3.50=21. So they sold 21 large pizzas and 17 small ones. SHAZAM! Am I not the most awesome? I am, aren't I? Look at the longass explanations others put up. No complicated crappy equations to solve, my way.

We can make a system of equations.
Let x = # of small pizzas sold
Let y = # of large pizzas sold

9x + 12.5y = 415.5
x + y = 38

Now, the (x + y = 38) part can be changed to a slope-intercept equation.

9x + 12.5y = 415.5
y = -x + 38

Now, we can solve by substituting the (-x + 38) in place of the (y) in the first equation.

9x + 12.5(-x + 38) = 415.5

9x - 12.5x + 475 = 415.5

-3.5x + 475 = 415.5

Subtract the 475 from both sides. It cancels out from the left side.

-3.5x = -59.5

Divide by -3.5
[x = 17]

Now, you substitute 17 in place of (x) in either equation. Let's do it for the 2nd equation.

17 + y = 38

Subtract the 17 from both sides. Cancels out from the left side.

[y = 21] (17 small, 21 large)

The pizza parlor sold 17 small pizzas and 21 large pizzas.

12.5l + 9s = 415.5...(1)

l + s = 38...(2)

(2) in to (1) for l gives:

12.5(38 - s) + 9s = 415.5

=> 475 - 3.5s = 415.5

so, 3.5s = 59.5

=> s = 59.5/3.5

=> s = 17

Then, l = 21

i.e. 21 large and 17 small pizzas are sold.

:)>

x+y=38
12.5x+9y=415.5

solve for y in the first equation:
y = 38-x
replace y in the second equation:
12.5x+9(38-x)=415.5
solve for x:
12.5x+342-9x=415.5
3.5x+342=415.5
3.5x=73.5
x=21

substitute x back into the first equation, solve for y:
(21)+y=38
y = 17

therefore, the pizza place sold 21 larges and 17 smalls

X = number large, Y = number small
X + Y = 38
12.5(X) + 9(Y) = 415.50

X = 38 - Y

12.5(38-Y) + 9(Y) = 415.50
I'll leave the rest to you as an exercise, it's just simple math from here.

L + S = 38
S = 38 - L

12.5L + 9S = 415.5
12.5L + 9(38 - L) = 415.5
12.5L + 342 - 9L = 415.5
3.5L = 73.5
L = 21
S = 17