Raisins worth $4.20/kg are mixed with dried fruit worth $6.90/kg to make a mix.....

Question

Raisins worth $4.20/kg are mixed with dried fruit worth $6.90/kg to make a mixture worth $5.20/kg. How many kilograms of raisins and how many kilograms of dried fruit must be used to make 10kg of the mixture?

Answer 1

4.2r + 6.9f = 5.2m

r + f = 10 = m

 

Isolate a variable:

r = 10 - f

 

So now to start plugging in variables:

4.2(10 - f) + 6.9f = 5.2 * 10

42 - 4.2f + 6.9f = 52

2.7f + 42 = 52

2.7f = 10

f = 100/27 (or 3 ¹⁹/₂₇) kg

 

r = 10 - 100/27

r = 270/27 - 100/27

r = 170/27 (or 6 ⁸/₂₇) kg

 

check

4.2 * 170/27 + 6.9 * 100/27 = 5.2 * 10

26.44 + 25.56 = 52

52 = 52