+0

0
105
4

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)

Mar 3, 2020
edited by Guest  Mar 3, 2020

#1
+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
0

Sorry for the "typo"!!. B should read 170 NOT 70. But the solution is correct.

Guest Mar 3, 2020
#3
0

it is ok

btw how old r u?

that was just a random question.

Guest Mar 3, 2020
#4
+111436
+1

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

Mar 3, 2020