SOLUTION: A candy distributor needs to mix a 30% fat-content chocolate with a 60% fat-content chocolate to create 100 kilograms of a 36% fat-content chocolate. How many kilograms of each kin

Click here to see ALL problems on Length-and-distance

Question 1162558: A candy distributor needs to mix a 30% fat-content chocolate with a 60% fat-content chocolate to create 100 kilograms of a 36% fat-content chocolate. How many kilograms of each kind of chocolate must they use?
Found 3 solutions by jim_thompson5910, greenestamps, josgarithmetic:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!

Answer:
80 kilograms of the 30% fat content chocolate
20 kilograms of the 60% fat content chocolate

====================================================================
Work Shown:

We have two kinds of chocolate, which we'll call A and B
x = amount of chocolate A
y = amount of chocolate B
amounts are in kilograms
x+y = total amount of chocolate from both candies
x+y = 100, since we want 100 kg total
y = -x+100, solve for y

0.30x = amount of pure fat from chocolate A
0.60y = amount of pure fat from chocolate B
0.30x+0.60y = total amount of pure fat from both chocolates combined
0.30x+0.60y = 0.36*100
0.30x+0.60y = 36
the expression 0.36*100 represents 36% of the total amount 100 kg is pure fat. So we have 36 kg of pure fat

Plug in y = -x+100. Solve for x.
0.30x+0.60y = 36
0.30x+0.60( y ) = 36
0.30x+0.60( -x+100 ) = 36 ... replace y with -x+100
0.30x-0.60x+60 = 36 ... distribute
-0.30x+60 = 36
-0.30x = 36-60
-0.30x = -24
x = -24/(-0.30)
x = 80

We can now find the value of y with this x value
y = -x+100
y = -80+100
y = 20

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

Let x be the number of kg of the 30% fat content chocolate; then the number of kg of 60% fat content chocolate is (100-x).

He is mixing x kg of 30% fat with (100-x) kg of 60% fat to obtain 100 kg of 36% fat:

Solve using basic algebra (I leave that to you)....

Here is a quick and easy non-algebraic method you can use to find the solution to this problem, or any other two-part mixture problem.

(1) On a number line, 36% is 1/5 of the way from 30% to 60%. (From 30 to 60 is a difference of 30; from 30 to 36 is a difference of 6. 6/30 = 1/5.)

(2) That means 1/5 of the mixture is the chocolate with the higher percentage fat content.

ANSWER: 1/5 of the 100kg, or 20kg, of the 60%; the other 80kg of the 30%.

CHECK:
.60(20)+.30(80) 12+24 = 36
.36(100) = 36

Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
Q of the 60% fat candy
100-Q of the 30% fat candy

-

--------------How much of the 60% fat candy; the numeric simplifications carried out to THIS extent for a reason.

Continuing:

.