A tailor used $30$ butlots that had actually an average (Arithmetic mean) weight of $x$ grams per switch and $20$ other butloads that had actually an average weight of $80$ grams per button. Which Of the following is the average weight per button, in grams, of the $50$ buttons that the tailor used?

$x+(20)(80)/50$$x+80/50$$3/5x+8/5$$3/5x+32$$5/8x$

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Survey the Question

Let’s search the problem for clues regarding what it will be testing, as this will help change our minds to think about what kind of math understanding we’ll usage to settle this question. Pay attention to any type of words that sound math-certain and anypoint one-of-a-kind about what the numbers look prefer, and note them on our paper.

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The question asks us to find the average weight of a set of butlots, which is a great indication that we’ll draw upon our expertise of Numerical Methods for Describing Data GRE math ability. Let’s store what we’ve learned about this ability at the tip of our minds as we method this question.

What Do We Know?

Let’s carefully read with the question and also make a list of the things that we recognize.

We have $30$ buttons through an average weight of $x$ grams per buttonWe have $20$ other butlots with an average weight of $80$ grams per buttonWe desire to discover the average weight of all $50$ buttons

Develop a Plan

We want to discover the average weight of $50$ butloads. We understand that to find an average, we take the sum of a collection of values and also divide by the number of worths. So for our question, we have:

$$Mean Weight of 50 Butlots = Sum of he Weights of 50 Buttons/50$$

So if we deserve to uncover the sum of the weights of every one of the butloads, we have the right to calculate the average button’s weight. We understand that the full amount of every one of the weights of the butloads will certainly be the sum of the weights for the $30$ buttons and the $20$ butloads.

$$Sum of he Weights of 50 Butloads = Sum of he Weights of 20 Buttons + Sum of he Weights of 30 Buttons$$

We recognize that the average weight of the $20$ butlots is $80$ grams per button. So we have the right to find the amount of the weights of the $20$ buttons by multiplying the average weight of them by the variety of buttons:


$$Sum of he Weights of 20 Buttons = 20·80$$

Similarly, we know that the amount of the weights of the $30$ buttons will certainly be the product of their average weight, which is $x$, and also number of buttons:

$$Sum of he Weights of 30 Butloads = 30·x$$

Let’s combine these two sums of weights together to get the full weight of the butlots, then we deserve to divide by $50$ to obtain the average weight of the butlots.

Solve the Question

We’ll begin through our in its entirety equation for the average weight of the $50$ buttons, then plug in the equations and numbers we occurred.

$Mean Weight of 50 Buttons$$=$$Sum of he Weights of 50 Buttons/50$
$Typical Weight of 50 Buttons$$=$$Sum of he Weights of 20 Butlots + Sum of he Weights of 30 Buttons/50$
$Typical Weight of 50 Buttons$$=$$20·80+30·x/50$
$Median Weight of 50 Buttons$$=$$20·80/50+30·x/50$
$Mean Weight of 50 Buttons$$=$$32+3/5x$

Looking at our answer options, we deserve to check out that the correct answer is D, $3/5x+32$.

What Did We Learn

For inquiries entailing an average, we have to keep our minds flexible. There’s a great possibility that the question might be more easily addressed if we transform the average to a amount. Let’s remember that just because a question is worded a specific way, that doesn’t pigeonhole us right into just being able to think of the question that means.

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