SOLUTION: Amy is making small and large hamburger patties to store in her freezer. A small hamburger patty uses 1/6 pound and a large patty uses 1/3 pound of ground beef. She wants to make t

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Question 1150810: Amy is making small and large hamburger patties to store in her freezer. A small hamburger patty uses 1/6 pound and a large patty uses 1/3 pound of ground beef. She wants to make twice as many large patties as small patties. Using 10 pounds of ground beef, how many of each type of patty can she make?
Found 3 solutions by MathLover1, josgarithmetic, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
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let the number of the small hamburger patties be x and the number of the large hamburger patties y
given:
a small hamburger patty uses 1%2F6 pound of ground beef: total %281%2F6%29x
a large patty uses 1%2F3 pound of ground beef: total %281%2F3%29y
if she wants to make twice as many large patties as small patties, than
y=2x.....eq.1
if she using 10 pounds of ground beef, than
%281%2F6%29x%2B%281%2F3%29y=10......eq.2

substitute y from eq.1

%281%2F6%29x%2B%281%2F3%292x=10.............solve for x
x%2F6%2B2x%2F3=10.........both sides multiply by 6
x%2B4x=60
5x=60
x=highlight%2812%29-> the number of the small hamburger patties

go to y=2x.....eq.1 substitute x
y=2%2A12
y=highlight%2824%29-> the number of the large hamburger patties

check:

%281%2F6%29x%2B%281%2F3%29y=10......eq.2
%281%2F6%2912%2B%281%2F3%2924=10
2%2B8=10
10=10



Answer by josgarithmetic(39618) About Me  (Show Source):
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c, number of small
g, number of large

system%28%281%2F6%29c%2B%281%2F3%29g=10%2Cg=2c%29
Simplify and solve the system.
---
---
6%28c%2F6%2Bg%2F3%29=6%2A10
c%2B2g=60
substitute for g
c%2B2%2A2c=60
5c=60
highlight%28c=12%29----------how many small patties
evaluate g
g=2c
g=2%2A12
highlight%28g=24%29----------how many large patties

Answer by greenestamps(13200) About Me  (Show Source):
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Since she wants to make twice as many large patties as small patties, consider one "batch" consisting of two large patties and one small patty.

The weight of one of those batches is 2(1/3)+1(1/6) = 5/6 pounds.

The number of batches she can make with 10 pounds of ground beef is 10(5/6) = 10*(6/5) = 12.

Since each batch contains 2 large patties and 1 small patty, with 10 pounds of ground beef she can make 20 large patties and 10 small patties.