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How many pounds of candy that sells for
$3.25 per lb must be mixed with candy that sells for
$2.75 per lb to obtain
20lb of a mixture that should sell for
$3.15 per lb?

How many pounds of candy that sells for $\$3.25$ per $lb$ must be mixed with candy that sells for $\$2.75$ per $lb$ to obtain $20$ $lb$ of a mixture that should sell for $\$3.15$ per $lb$ ?

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Weighted averages: word problems

Full solution

Q. How many pounds of candy that sells for

\$3.25

per

lb

must be mixed with candy that sells for

\$2.75

per

lb

to obtain

20

lb

of a mixture that should sell for

\$3.15

per

lb

?

Denote candy amounts: Let's denote the amount of $\$3.25$ per pound candy as $x$ pounds. Then, the amount of $\$2.75$ per pound candy would be $(20 - x)$ pounds, since the total weight of the mixture is $20$ pounds.
Calculate total cost: The total cost of the $x$ pounds of $\$3.25$ candy is $3.25x$ dollars.
Set up equation: The total cost of the $20 - x$ pounds of $\$2.75$ candy is $2.75(20 - x)$ dollars.
Distribute and simplify: The total cost of the $20$ pounds of the mixture that sells for $\$3.15$ per pound is $3.15 \times 20$ dollars.
Combine like terms: We can set up an equation to represent the total cost of the mixture from both types of candy: $3.25x + 2.75(20 - x) = 3.15 \times 20$ .
Isolate term with x: Now, let's distribute and simplify the equation: $3.25x + 55 - 2.75x = 63$ .
Solve for x: Combine like terms: $0.50x + 55 = 63$ .
Calculate x: Subtract $55$ from both sides to isolate the term with $x$ : $0.50x = 63 - 55$ .
Calculate x: Subtract $55$ from both sides to isolate the term with $x$ : $0.50x = 63 - 55$ . Solve for $x$ : $0.50x = 8$ .
Calculate x: Subtract $55$ from both sides to isolate the term with $x$ : $0.50x = 63 - 55$ . Solve for $x$ : $0.50x = 8$ . Divide both sides by $0.50$ to find $x$ : $x = \frac{8}{0.50}$ .
Calculate x: Subtract $55$ from both sides to isolate the term with $x$ : $0.50x = 63 - 55$ . Solve for $x$ : $0.50x = 8$ . Divide both sides by $0.50$ to find $x$ : $x = \frac{8}{0.50}$ . Calculate $x$ : $x = 16$ .

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