The ratio of the number of $2-notes to $20-notes in Elyse's purse was 1 : 3. Elyse exchanged 8 pieces of $20-notes for $2-notes. She then had an equal number of $2-notes and $20-notes. What was the total value of $2-notes and $20-notes in Elyse's purse at first?
|
$2-notes |
$20-notes |
Before |
1 u |
3 u |
Change |
+ 80 |
- 8 |
After |
1 u + 80 |
3 u - 8 |
Value of 8 pieces of $20-notes
= 8 x 20
= $160
Number of $2-notes that Elyse exchanged for
= 160 ÷ 2
= 80
After the exchange, Elyse had an equal number of $2-notes and $20-notes.
3 u - 8 = 1 u + 80
3 u - 1 u = 80 + 8
2 u = 88
1 u = 88 ÷ 2 = 44
Number of $2-notes at first
= 1 u
= 44
Value of $2-notes at first
= 44 x 2
= $88
Number of $20-notes at first
= 3 u
= 3 x 44
= 132
Value of $20-notes at first
= 132 x 20
= $2640
Total value of $2-notes and $20-notes at first
= 88 + 2640
= $2728
Answer(s): $2728