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Sebastian has been saving part of his allowance in a bag every month. The bag containing $2 and $10 notes had a total value of $2280. 4 pieces of $10 notes were exchanged for $2 notes of the same value. In the end, the number of $10 notes was the same as the $2 notes. How many $2 notes were there at first?

 

(i don understand algebra so pls explain it in another way but its ok if u don no other ways u can just use algebra)

laugh

 Mar 3, 2020
edited by Guest  Mar 3, 2020
 #1
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+1

Let the number of $2 bills =B
The number of $10 bills    =T

 

2B + 10T = 2280.................(1)
T - 4 =B + 20.......................(2), solve for B, T


B = 70 - number of $2 bills originally
T =194 - number of $10 bills originally.

Note: When he exchanged 4 $10 bills for $2 bills, it means he lost 4 x $10 =$40 in 10-dollar bills. This $40 was exchanged into $40/$2 =20 2-dollar bills. In other words:4 x $10 =20 x $2. And that is what equation (2) means.

 Mar 3, 2020
 #2
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Sorry for the "typo"!!. B should read 170 NOT 70. But the solution is correct.

Guest Mar 3, 2020
 #3
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it is ok 

thks for your help 

btw how old r u?

that was just a random question.blushlaugh

Guest Mar 3, 2020
 #4
avatar+111436 
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Call the  original number   of  $10  notes,  M

Call the original number of  $2  notes , N

 

So

10M +  2N =  2280     (1)

 

If  4 pieces of  $10 notes were exchanged  for  $2  notes of the same value....then the  number of  $2  notes   must increase  by   20  since after  the exchange  and  the  number  of  $10 notes  must  decreases  by  4....and since we have the  same number after the  exchanges.....then 

 

So

 

M - 4  =   N +  20

M =  N +  24      (2)

 

Sub (2)  into (1)   and we have that

 

 

10 (N + 24)  + 2N  = 2280    simplify

 

10N  + 240  + 2N  = 2280     subtract   240  from both sides

 

12N  =  2040   divide  both sides  by 12

 

N  = 170    =  number of  $2  notes originally  

 

Proof

There  were   170  $2 notes originally  and 

10M  + 2 (170)   = 2280

10M + 340  = 2280

10m = 2280  - 340  = 

10M = 1940

M  = 194    $10  notes originally

 

After  the  exchange   there  are  170 + 20   = 190  $2  notes   and  194 - 4  = 190  $10 notes

 

 

cool cool cool

 Mar 3, 2020

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