amyhussein wrote:hello
how to solve the following question in a shorter simpler way
there is a total of 48 items with average cost of 51. The average cost of 32 items is 39 usd, what is the average cost of the remaining 16 items?
Approach 1: Plug in small values that satisfy the given ratio
32 items cost an average of $39, while the remaining 16 items cost an average of x dollars.
Since 32:16 = 2:1, for every 2 items that cost $39, 1 item costs x dollars.
Total cost of 3 items at an average cost of $51 per item = 3*51 = 153.
Total cost of 2 items at an average cost of $39 per item = 2*39 = 78.
Cost of the 1 remaining item = 153-78 = 75.
Approach 2: alligation
Let A = the $39 items and B = the items with an unknown average cost.
Step 1: Plot the costs on a number line, with the two ingredients on the ends and the average cost of the mixture in the middle.
A 39----------51---------B
Step 2: Plot the distances between the costs.
(distance between A and 51) : (distance between 51 and B) is equal to the RECIPROCAL of the ratio of A to B in the mixture.
Since A = 32 items and B = 16 items, A:B = 32:16 = 2:1.
Plotting the reciprocal of this ratio on the number line, we get:
A 39----
x-----51----
2x----B
Since x is the distance between A and 51:
x = 51-39 = 12.
Since 2x is the distance between 51 and B:
B = 51 + 2x = 51 + 2*12 = 75.
Other mixture problems:
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https://www.beatthegmat.com/mixture-prob ... tml#604126
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