Question 1012008: The average of one set of 4 numbers is 35. The average of another set of numbers is 20. The average of the numbers in the two sets is 30. How many numbers are in the other set?
Answer by ValorousDawn(53)   (Show Source):
You can put this solution on YOUR website! The sum of all the numbers in the first set is the number of numbers multiplied by the average. This is because average is defined as sum/#ofnumbers, and as such, if you multiply by the number of numbers, you end up with the sum. Therefore, the sum of the first set is 4*35=140.
The definition of average still holds, and as such, the number of terms is 4+x, with x being the number of numbers in the second set, the sum of the numbers is 140+20x. The 20x comes from the same logic of multiplying the average by the number of numbers to isolate the sum. Since we have the solution to this, the average, we can set them equal to eachother and solve.
140+20x/4+x=30
Multiply across by 4+x. (We know that x cannot be -4 because you cannot divide by zero, but a negative number of numbers is illogical, so disregard the restriction)
140+20x=120+30x
Subtract 120 and 2x from both sides to isolate the variable from the constants.
20=10x
x=2
We can check our answer to see if it verifies.
140+20(2)/4+(2)=30
180/6=30
Since the answer solves, the answer of 2 is correct.
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