A natural food store makes its own brand of trail mix out of dried apples, raisins, and peanuts. One pound of the mixture costs $3.18. It contains twice as much peanuts by weight as apples. One pound of dried apples costs $4.48, a pound of raisins $2.40, and a pound of peanuts $3.44. How many ounces of each ingredient are contained in 1 pound of the trail mix?

50.88

Step-by-step explanation:

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 = 12.48%2F4.16

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