Candy mixture problem

Question

A candy distributor needs to mix a 20% fat-content chocolate with a 50% fat-content chocolate to create 200 kilograms of a 39.5% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

Answer 1

ANSWER: 130 kg of 50% fat-content chocolate and 70 kg of 20% fat-content chocolate

Let a = amount of 20% fat-content chocolate and b = amount of 50% fat-content chocolate

Set up system of equations:

For total weight (Eqn. 1): a + b = 200

For weight of fat content (Eqn. 2): 0.2a + 0.5b = 200 (0.395)

Rearrange first equation:

a = 200 - b

Plug into second equation: (**note that this solution uses SUBSTITUTION but you can also use ELIMINATION or GRAPHING)

0.2(200 - b) + 0.5b = 200 (0.395)

Solve equation for b:

40 - 0.2b + 0.5b = 79

0.3b = 39 so b = 39/0.3 = 130 kg of 50% fat-content chocolate

Plug back in to Eqn. 1 to solve for a:

a + b = 200 so a = 200 - b = 200 - 130 = 70 kg of 20% fat-content chocolate

Answer 2

20% fat content chocolate has x weight

50% fat content chocolate has y weight

When the two are mixed, it results in 39.5% of 200 kg weight

(20/100) x + (50/100) y = (39.5 / 100) * 200 ------------ (1)

x + y = 200

= > y = 200 - x -------- (2)

substituting the value of y from equation (2) into equation (1)

0.2x + 0.5y = 79

=> 0.2x + (0.5 * (200 - x)) = 79

=> 0.2x + 100 - 0.5x = 79

=> 100 -79 = 0.3x

=> 21 = 0.3 x

=> x = 210 / 3 = 70 Kg of 20% fat content

Substituting the value of x = 70 K in equation (2)

y = 200 - x

y = 200 - 70 kg

y = 130 kg of 50% fat content chocolate