SOLUTION: At a candy store, Erika bought 3 kilograms of cinnamon red hots and 1 kilogram of gummy bears for $21.00. Meanwhile, Irene bought 3 kilograms of cinnamon red hots and 3 kilograms o

Question 1131850: At a candy store, Erika bought 3 kilograms of cinnamon red hots and 1 kilogram of gummy bears for $21.00. Meanwhile, Irene bought 3 kilograms of cinnamon red hots and 3 kilograms of gummy bears for $39.00. What is the cost of one kilogram of each type of candy?

Found 5 solutions by Boreal, stanbon, MathTherapy, josgarithmetic, greenestamps:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
cinnamon is C
gummy bears are B
3C+B=21
3C+3B=39
Note that 2 B increased $18, so B=9
alternatively subtract the second from the first
-2B=-18
B=$9 ANSWER
3C=12
C=$4 ANSWER
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
At a candy store, Erika bought 3 kilograms of cinnamon red hots and 1 kilogram of gummy bears for $21.00. Meanwhile, Irene bought 3 kilograms of cinnamon red hots and 3 kilograms of gummy bears for $39.00. What is the cost of one kilogram of each type of candy?
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Equations:
3r + 1g = 21.00
3r + 3g= 39.00
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Subtract and solve for "g"::
2g = 2.00
g = $1.00/kg (gummy bear cost)
---------
Solve for "r":
3r + g = 21
3r + 1 = 21
r = $20/3 = $6.67/kg (red hot oost)
Cheers,
Stan H.
Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!
At a candy store, Erika bought 3 kilograms of cinnamon red hots and 1 kilogram of gummy bears for $21.00. Meanwhile, Irene bought 3 kilograms of cinnamon red hots and 3 kilograms of gummy bears for $39.00. What is the cost of one kilogram of each type of candy?

STANBON'S answers are WRONG, and don't make any sense, whatsoever!
Answer by josgarithmetic(39628)   (Show Source): You can put this solution on YOUR website!
c, Cinnamon red hots price
g, Gummy bears price

Equation2 - Equation1

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Simplify equation2,

-
Cinnamon Red Hots, $9 per kilogram
Gummy Bears, $4 per kilogram
Answer by greenestamps(13206)   (Show Source): You can put this solution on YOUR website!

Using formal algebra on this problem is good exercise in learning how to solve problems using algebra.

However, note that the formal algebraic solution does exactly what you can do informally with logical reasoning.

The difference between the two purchases was 2 additional kg of gummy bears for an additional $18; that means the cost of the gummy bears is $9 per kg.

Then, knowing that, you can use either of the purchases to find the cost per pound of the cinnamon red hots. For example, Erika bought 3 kg of cinnamon red hots and 1 kg of gummy bears for $21; the gummy bears cost $9, so the 3 kg of cinnamon red hots cost $12; so the cinnamon red hots cost $4 per kg.
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