Question

Leanne, owner of The Candy Shoppe, wants to make 16-ounce gift bags with a mix of hard peppermint candies and chocolate mints. If peppermints cost 6¢ per ounce and the chocolate mints 22¢ per ounce, how many of each are in a gift bag that costs $2.72?​

Answer 1

The gift bag contains 5 ounces of peppermint candies and 11 ounces of chocolate mint.

Step-by-step explanation:

Cost of peppermint candies per ounce = 6 cents

Cost of chocolate mint = 22 cents

Cost of bag = $2.72 = 2.72*100 = 272 cents

Weight of bag = 16 ounce

Let,

x be the ounces of peppermint candies

y be the ounces of chocolate mint

x+y=16     Eqn 1

6x+22y=272    Eqn 2

Multiplying Eqn 1 by 6

$6(x+y=16)\\6x+6y=96\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(6x+22y)-(6x+6y)=272-96\\6x+22y-6x-6y=176\\16y=176$

Dividing both sides by 16

$\frac{16y}{16}=\frac{176}{16}\\y=11$

Putting y=11 in Eqn 1

$x+11=16\\x=16-11\\x=5$

The gift bag contains 5 ounces of peppermint candies and 11 ounces of chocolate mint.

Keywords: linear equation, subtraction

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