Question

A mixture of 30 pounds of candy sells for $1.10 a pound. The mixture consists of chocolates worth $1.50 a pound and chocolates worth 90¢ a pound. How many pounds of the $1.50 chocolate were used to make the mixture? If x represents the pounds of $1.50 chocolates used, then which of the following represents the pounds of 90¢ chocolates used?

Answer 1

A mixture of 30 pounds of candy sells for $1.10 a pound. The mixture consists of chocolates worth $1.50 a pound and chocolates worth 90¢ a pound.

Let x be the chocolate worth $1.50 per pound

Let y be the chocolate worth $0.90 per pound        ( ∵ 90¢ = $0.90 )

Therefore, we have,

x + y = 30 ..........(1)

As mixture of 30 pounds of candy sells for $1.10 a pound, we have,

⇒ ( 1.5x + 0.9y ) / (x + y) = 1.10

1.5x + 0.9y = 1.10 (x + y)

1.5x + 0.9y = 1.10x + 1.10y

1.5x - 1.10x = 1.10y - 0.9y

0.4x - 0.2y = 0 ...........(2)

solving equations (1) and (2), we get,

y = 20

x = 10

Therefore, 10 pounds of the $1.50 chocolate and 20 pounds of the 90¢ were used to make the mixture.