Breakfast Cereal Math Question

Question

A grocer wants to make a natural breakfast cereal mix that he will sell for $3.75 per kilogram by mixing 15 kilograms of dried fruit worth $9 per kilogram with oat cereal worth $2 per kilogram. How many kilograms of the oat cereal will he have to use?

Answer 1

Start by listing what you know and the unknowns:

kilograms of dried fruit = 15

kilograms of oat cereal = x

total kilograms in mixture = 15+x

Now calculate how much the dried fruit, oat cereal, and mixture would cost:

dried fruit = 15*9

oat cereal = x*2

mixture = (15+x)*3.75

The cost of the mixture should equal the sum of the cost of the dried fruit and the oat cereal:

(15+x)*3.75=(15*9)+(x*2)

Simplify:

56.25+3.75x=135+2x

1.75x=78.75

x=45

He will have to use 45 kilograms of the oat cereal. Make sure to check your work by plugging in this value of x into the equation!

Answer 2

let x = kg of oat cereal

15*9 = $135 worth of fruit

2x = $2x worth of oats

15+x kg worth of fruit and oats at 3.75$ per kg:

15*9 + 2x = 3.75(15+x)

135 + 2x = 56.25 + 3.75x

1.75x = 78.74

x = 45

45 kg of oats

Check:

15 kg of fruit at $9 ($135) + 45 kg of oats at $2 (90)/( 15 kg + 45 kg) = 225$/60 kg = $3.75/kg