SOLUTION: 1/2 of a pepperoni pizza + 3/4 of a ham pizza contains 765 calories. 1/4 of a pepperoni pizza + one whole ham pizza contains 745 calories. How many calories are in a whole pepper

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 1/2 of a pepperoni pizza + 3/4 of a ham pizza contains 765 calories. 1/4 of a pepperoni pizza + one whole ham pizza contains 745 calories. How many calories are in a whole pepper      Log On


   

Question 398627: 1/2 of a pepperoni pizza + 3/4 of a ham pizza contains 765 calories.
1/4 of a pepperoni pizza + one whole ham pizza contains 745 calories.
How many calories are in a whole pepperoni pizza?
How many calories are in a whole ham pizza?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let a pepperoni pizza be x and a ham pizza be y

%281%2F2%29x+%2B+%283%2F4%29y+=+765cal.....(1)
%281%2F4%29x+%2B+y+=+745cal........(2)
-----------------------------------------solve this system


%281%2F2%29x+%2B+%283%2F4%29y+=+765cal.....(1)solve for x

4%281%2F2%29x+%2B+4%283%2F4%29y+=+4%2A765cal.
cross%284%292%281%2Fcross%284%29%29x+%2B+cross%284%29%283%2Fcross%284%29%29y+=+3060cal.

2x+%2B+3y+=+3060cal.

2x+=3060cal-3y.....divide by 2

x++=+1530cal-%283y%2F2%29.....plug it in (2) and solve for y


%281%2F4%29x+%2B+y+=+745cal........(2)

%281%2F4%29%281530cal+-%283%2F2%29y%29+%2B+y+=+4%2A745cal...........multiply by 4

4%281530cal%2F4%29+-+4%281%2F4%29%283%2F2%29y+%2B+4y+=+4%2A745cal.
1530cal+-+%283%2F2%29y+%2B+4y+=+2980cal.
1530cal+-+1.5y+%2B+4y+=+2980cal.
1530cal+%2B%283.5%29y+=+2980cal.


+%283.5%29y+=+2980cal-1530cal

+%283.5%29y+=+1450cal

+y+=+1450cal%2F%283.5%29

+y+=+414.3cal

now find x


x++=+1530cal+-+3y%2F2.
x++=+1530cal+-+3%28414.3cal%29%2F2.
x++=+1530cal+-+621.45cal.
x++=+908.55cal.

check:
%281%2F2%29x+%2B+%283%2F4%29y+=+765cal.....(1)
%281%2F2%29908.55cal+%2B+%280.75%29414.3cal+=+765cal
454.275cal+%2B+310.725cal+=+765cal
765cal++=+765cal