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In a certain candy store, 3 pounds of candy and 2 pounds of mints cost $10.80, and 1 pound of candy and 3 pounds of mints cost $5.35. What is the cost per pound of the mints?

mints are 65¢ per lb
mints are 75¢ per lb
mints are 85¢ per lb

2 Answers

5 votes

Answer:The correct answer to this problem would be that:

mints are 75 cents per lb.

Explanation:

User Helq
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3 votes
This is an application of linear equations in two variables

Let c = candies(in pounds) ; m = mints(in pounds also)

From this sentence >> 3 pounds of candy and 2 pounds of mints cost $10.80

you can make-up an equation >> 3c + 2m = 10.80 right?

That's your first equation, 3c + 2m = 10.80 ... (1)


and from this sentence >> 1 pound of candy and 3 pounds of mints cost $5.35

you can make-up an equation >> c + 3m = 5.35 ... (2)

you can use various methods here, like graphing, substitution, comparison, and elimination method.

Let's try using substitution method.

3c + 2m = 10.80 ... (1)
c + 3m = 5.35 ... (2) << here you can come up with c = 5.35 - 3m then substitute it to (1)

3c + 2m = 10.80 ... (1)
3(5.35 - 3m) + 2m = 10.80
16.05 - 9m + 2m = 10.80
-7m = -5.25
m = 0.75 <<This is the price of the mint

to get the price of candy, simply substitute m = 0.75 to (1) or (2) if you want, it depends on you.

Either way, you will have the same answer.

Let's try substituting in (1)

3c + 2m = 10.80 ... (1)

3c + 2(0.75) = 10.80

3c + 1.5 = 10.80

3c = 9.3

c = 3.1 <<this is the price of the candy
User ZSG
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