Question

Milk and cream are mixed together for a recipe. The total volume of the mixture is 1 cup. If the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat, how much cream is in the mixture?

Answer 1

1 = M + C

(2/100)* M + (18/100)*C = 6/100

2 equations, 2 unknowns

Answer 2

Is that what you are studying at the time? Systems of equations?

Answer 3

yes

Answer 4

Ok, the hard part i am guessing, is translating the paragraph into the equations right?

Answer 5

oh cool thx

Answer 6

Here..

Answer 7

Define the variables first...

Let M = cups of milk
C = cups of cream

Answer 8

The total volume of the mixture is 1 cup

Total Mixture = Cups of Cream + Cups of Milk

1 Cup = C cups of cream + M cups of milk

1 = C + M

Answer 9

If the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat

(Fat From Milk)*(Cups of milk) + (fat From Cream)*(Cups of Cream) = Fat in mixture

(0.02)*M + ( 0.18)*C = (0.06)

Answer 10

So the 2 equations to be solved are

C + M = 1
(0.02)*M + ( 0.18)*C = (0.06)

For C cups of cream, and M cups of milk..

Answer 11

you with me so far?

Answer 12

Solve first equation for either M or C, i will solve it for C.

M + C = 1

C = 1 - M

Substitute C = 1 - M into the second equation

(0.02)M + 0.18*(1 - M) = 0.06

Answer 13

One variable in one equation, we can solve for the M cups of milk

0.02M + 0.18 - 0.18M = 0.06

-0.16M = -0.12

M = (-0.12)/(-0.16)

M = 0.75 cups of milk

Answer 14

If M = 0.75 cups milk, then from the first equation, the total mixture is 1 cup

M + C = 1

0.75 + C = 1

C = 1 - 0.75

C=0.25 cups Cream

Answer 15

The mixture contains

0.75 cups of Milk
0.25 cups of cream

Answer 16

@aeh101