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The student council sold 661 T-shirts, some at $10 and some at $12. When recording the amount of T-shirts they had sold at each of the two prices, they reversed the amounts. They thought they made $378 more than they really did. How many T-shirts actually were sold at $10 per shirt?

 May 22, 2020
 #1
avatar+744 
0

Well, since x = 10 dollar shirts

Then:

661 - x = 12 dollar shirts

10x + 12 (661-x)  + 378 = 12x + 10(661-x)

10x +7932 - 12x + 378 = 12x +6610 -10x

 

So: x = 425    shirts at $10

Hope this helps, whymenotsmart^m^.

 May 22, 2020
 #2
avatar+978 
+2

So let's say x is the money they made at 10 dollars(a) and 12(b). The two variables are for the number sold.

 

They reversed it so that it was 12(a) and 10(b).

 

Thus

 

12a +10b = 10a + 12b + 378

 

Some rearrangement:

 

12a +10b - 10a -12 b = 378

 

2a - 2b = 378

 

a-b = 189

 

So we sold 661 tshirts.

 

661-189= 472,/2 = 236

 

So b = 236 and a = 236 + 189 = 425.

 

425*10 + 236*12 = 7082

 

Flip around, 425* 12 + 236 * 10 = 7460.

 

7460- 7082 = 278.

 

Thus 425 at 10, 236 at 12.

 

if you don't understand anything feel free to ask.

 

Great solution, whymeissmart hehehe

 May 22, 2020
 #3
avatar+744 
0

thanks, you too, maybe I should change my name, so you would stop making fun of me (JK....)!!

 May 22, 2020
 #4
avatar+978 
+1

I actually don't think that's possible...

 

Whymenottnewton


LOL

 

I can do this all day!

hugomimihu  May 22, 2020
edited by hugomimihu  May 22, 2020
 #5
avatar+744 
0

LOL, for some reason, titaniumrome is in the leaderboard now, for some reason, but then I scroll down for leaderboards rom is in the leaderboards, you know what I mean, hugo??

 May 22, 2020
edited by whymenotsmart  May 22, 2020
 #6
avatar+978 
+1

Eh it must be a glitch.

hugomimihu  May 22, 2020

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