A party mix is made by adding nuts that sell for ​$2.50 per kg to a cereal mixture that sells for ​$1 per kg. How much of each should be added to obtain 30kg of a mix that will sell for ​$1.90 per​ kg

Question

A party mix is made by adding nuts that sell for

​$2.50

per kg to a cereal mixture that sells for

​$1

per kg. How much of each should be added to obtain

30

kg of a mix that will sell for

​$1.90

per​ kg?

Answer 1

2.5x + 1(30-x) = 1.9(30)

2.5x -x = 1.9(30)-1(30)

1.5x = .9(30) = 27

x = 27/1.5= 9/.5

x = 18 kg of $2.50 mixed with 12 kg of $1 to get 30 kg of $1.90 mix

1 is within .9 of 1.9

2.5 is within .6 of 1.9

.9/.6 = 3/2 = 18/12

you need 1 1/2 times as much of $2.50 as $1

2.5(18) + 1(12) = 45+12 = 47 = 1.9(30) = 47