# Calculating average of word problem

I was preparing for a standardized test and came across the following problem:

During a closeout sale 30 suits are sold at \$60 each.The price is the reduced to \$50 each and 20 suits are sold. At what average price must the remaining 10 suits be sold in order to obtain an average of \$55 for the 60 suits? The answer is supposed to be \$50. Could anyone tell me how they got that? A little working shown would be appreciated..

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Up to now 50 suits are sold for \$2800 alltogether. Now find$x$with$(2800 + 10x)/60 = 55$. – martini May 22 '12 at 15:24 ## 1 Answer The first and most important step is to introduce a variable:$\ \ \ \ \ \ $Let$x$be the common price of each of the remaining$10$suits. The second step is to find an equation in$x$. Of course, we may obtain one by knowing that the average sale price of the twenty suits is$55$dollars. Once we have our equation, we'll solve it for$x$. The average sale price of the suits is obtained by computing the total revenue from the$60$suits and dividing by$60$. Let's find the total revenue first. Thirty suits were sold at$60$dollars and twenty suits were sold at$50$dollars. The revenue from these is$30\cdot60+20\cdot 50$dollars. The remaining ten suits are sold at$x$dollars and the revenue from these is$x\cdot10$dollars. So, adding these together, the total revenue from the$60$suits is$30\cdot 60+ 20 \cdot 50 +x\cdot 10$dollars. Thus, the average sale price of the twenty suits is $$\tag{1}{\text{total revenue}\over 60}={30\cdot 60+ 20 \cdot 50 +x\cdot 10\over 60}.$$ Now we find our equation. You want$(1)$to turn out to be$55$. So set $$\tag{2} {30\cdot 60+ 20 \cdot 50 +x\cdot 10\over 60}=55.$$ Now the third and final step: we solve equation$(2)$for$x$. Towards that end, first multiply both sides of$(2)$by$60$: $${30\cdot 60+ 20 \cdot 50 +x\cdot 10 }=55\cdot 60.$$ Simplify the arithmetic: $$\tag{3} 2800+10x=3300,$$ or, subtracting$2800$from both sides of$(3)$, $$\tag{4} 10x=500.$$ Finally, divide both sides of$(4)$by$10$to obtain$x=50\$ dollars.

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OMG - Why couldn't I see this ... Thank you. – Rajeshwar May 22 '12 at 15:40
@Rajeshwar You're welcome; glad to help. – David Mitra May 22 '12 at 15:43