SOLUTION: A 20.80 gift box of candy contains 2 varieties. One type costs 1.60/kg and the other costs $1.80/kg. The number of kg at 1.80 is twice the number of kg as $1.60. Find the number of

Question 1205576: A 20.80 gift box of candy contains 2 varieties. One type costs 1.60/kg and the other costs $1.80/kg. The number of kg at 1.80 is twice the number of kg as $1.60. Find the number of kg of each type of candy.
Found 4 solutions by ikleyn, CharcoalRobin, greenestamps, josgarithmetic:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
A 20.80 gift box of candy contains 2 varieties.
One type costs 1.60/kg and the other costs $1.80/kg.
The number of kg at 1.80 is twice the number of kg at $1.60.
Find the number of kg of each type of candy.
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x kilograms at $1.60 per kilo. 2x kilograms at $1.80 per kilo. Total money equation 1.60*x + 1.80*(2x) = 20.80 dollars. Simplify and find x 1.60x + 3.60x = 20.80 5.20x = 20.80 x = 20.80/5.20 = 4. ANSWER. 4 kilograms candy at $1.60 and 2*4 = 8 kilograms candy at $1.80.

Solved.

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The solution of the other person has arithmetic ERRORS and, THEREFORE, is INCORRECT.

Answer by CharcoalRobin(1)   (Show Source): You can put this solution on YOUR website!
Variety Type 1, T1 which is $1.60/kg, and Variety Type 2, T2 which is $1.80/kg, Since we know there are two types of varieties that the gift box contains, for the first equation, we can sum the two Types together with their respective prices for (i.e. the cost of the gift box). The second equation can be found from the relation that Variety Type 2 is "twice the number" as Variety Type 1, therefore the second equation would be , where T1 and T2 are variables corresponding to their respective prices. Since we know that T2 = 2T1, we can substitute in for T2 for the first equation, using the second. So, , Then, , Combining Like Terms, and we have , Hence, . Now we can either substitute our value of T1 in for the first or second equation, but it will be easier to substitute T1 into the second equation, as there are less steps needed to take in order to evaluate what T2 is. Solving for T2, , and finally, . Now that we have solved for T1 and T2, we now know the respective amount of weight of each Type of Variety. In other words, T1 represents the "number of kg" of the first Type of candy, whereas T2 represents the "number of kg" of the second Type of candy.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

For new tutor CharcoalRobin....

(1) Learn how to use html to make your posts readable. Your post with the whole solution in a single paragraph is extremely hard to read.

You can learn some of the basics by looking at the responses from other tutors and clicking on "show source".

(2) Check you work and your answer before submitting your response. We are all capable of making arithmetic errors....

Here is an informal mental solution that solves the problem by the same path as the formal algebraic solution shown by tutor @ikleyn.

Since there are twice as many of the candies at $1.80/kg as there are at $1.60/kg, make groups of 2kg at $1.80/kg and 1kg at $1.60/kg, costing a total of 2($1.80)+$1.60 = $5.20.

Since the total cost is $20.80, the number of these groups is $20.80/$5.20 = 4.

So there are 4*2 = 8kg of candies at $1.80/kg and 4kg at $1.60/kg.

ANSWER: 8kg at $1.80/kg and 4kg at $1.60/kg

CHECK: 8($1.80)+4($1.60) = $14.40+$6.40 = $20.80

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
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A 20.80 gift box of candy contains 2 varieties.
One type costs 1.60/kg and the other costs $1.80/kg.
The number of kg at 1.80 is twice the number of kg as $1.60.
--------------

"A 20.80 gift box of,..."
Is this DOLLARS?
x kilograms of the $1.6 per kg type
2x kilograms of the $1.8 per kg type

Accounting for the price of the 20.80 DOLLAR gift box

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4 kilograms of the $1.6 per kg candy
8 kilograms of the $1.8 per kg candy
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