Question 167720: a natural food store makes its own brand of trial mix, out of dried apples,raisins and peanuts. One pound of the mixture is $3.18 it contains twice as much peanuts by weight than apples. One pound of dried apples cost $4.48, a pound of raisins cost $2.40 and a pound of peanuts is $ 3.44. How many ounces of each ingredient are contained in one pound of the trail mix?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! dried apples,raisins and peanuts. One pound of the mixture is $3.18
it contains twice as much peanuts by weight than apples.
:
One pound of dried apples cost $4.48, a pound of raisins cost $2.40 and
a pound of peanuts is $ 3.44.
:
How many ounces of each ingredient are contained in one pound of the trail mix?
:
Here it is, step-by-step
:
Let a = no. of oz of apples
Let r = no. of oz of raisins
Let p = no. of oz of peanuts
:
The equation:
4.48a + 2.40r + 3.44p = 3.18(16)
:
It says p = 2a, substitute 2a for p
4.48a + 2.40r + 3.44(2a) = 3.18(16)
:
4.48a + 2.40r + 6.88a = 50.88
:
4.48a + 6.88a + 2.40r = 50.88
:
11.36a + 2.40r = 50.88
:
At this point we can say: r = (16-3a), a represents apples & peanuts here.
Substitute (16-3a) for r, solve for a;
11.36a + 2.40(16-3a) = 50.88
:
11.36a + 38.40 - 7.2a = 50.88
:
11.36a - 7.2a = 50.88 - 38.40
:
4.16a = 12.48
a = 
a = 3 oz dried apples
then
P = 2(3)
P = 6 oz of peanuts
:
Find r:
r = 16 - 3 - 6
r = 7 oz of raisins
;
:
Check these values for a, r, p in the cost equation
4.48(3) + 2.40(7) + 3.44(6) = 3.18(16)
13.44 + 16.8 + 20.64 = 50.88; confirms our solutions
|
|
|
