A shopkeeper packages together two types of hard candy: peppermint and cinnamon. Separately the peppermint candy sell for $1.80/kg and the cinnamon candy sells for $2.40/kg. The mixture sells for $2.16/kg. Determine the amount of each type of candy that is required to make 50kg of the mixture. Verify your answer.

Question

A shopkeeper packages together two types of hard candy: peppermint and cinnamon. Separately the peppermint candy sell for $1.80/kg and the cinnamon candy sells for $2.40/kg. The mixture sells for $2.16/kg. Determine the amount of each type of candy that is required to make 50kg of the mixture. Verify your answer.
-Determine a linear equation to represent the total mass of the new mixture.
-Determine a linear equation to represent the cost of the new mixture.
-Apply a process to verify the point of intersection

Steve · Accepted Answer

we have p kg of peppermint and c kg of cinnamon

p+c=50, so c = 50-p

the price of all the peppermint + the price of the cinnamon is the price of all the mixed bags.

1.80p + 2.4(50-p) = 2.16(50)
1.80p + 120 - 2.4p = 108
.60p = 12
p = 20
so,
c = 30