The ratio of the number of $2-notes to $20-notes in Yen's wallet was 1 : 3. Yen exchanged 6 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 Yen's wallet at first?
| |
$2-notes |
$20-notes |
| Before |
1 u |
3 u |
| Change |
+ 60 |
- 6 |
| After |
1 u + 60 |
3 u - 6 |
Value of 6 pieces of $20-notes
= 6 x 20
= $120
Number of $2-notes that Yen exchanged for
= 120 ÷ 2
= 60
After the exchange, Yen had an equal number of $2-notes and $20-notes.
3 u - 6 = 1 u + 60
3 u - 1 u = 60 + 6
2 u = 66
1 u = 66 ÷ 2 = 33
Number of $2-notes at first
= 1 u
= 33
Value of $2-notes at first
= 33 x 2
= $66
Number of $20-notes at first
= 3 u
= 3 x 33
= 99
Value of $20-notes at first
= 99 x 20
= $1980
Total value of $2-notes and $20-notes at first
= 66 + 1980
= $2046
Answer(s): $2046
