The ratio of the number of $10-notes to $20-notes in Gem's handbag was 1 : 4. Gem exchanged 12 pieces of $20-notes for $10-notes. She then had an equal number of $10-notes and $20-notes. What was the total value of $10-notes and $20-notes in Gem's handbag at first?
| |
$10-notes |
$20-notes |
| Before |
1 u |
4 u |
| Change |
+ 24 |
- 12 |
| After |
1 u + 24 |
4 u - 12 |
Value of 12 pieces of $20-notes
= 12 x 20
= $240
Number of $10-notes that Gem exchanged for
= 240 ÷ 10
= 24
After the exchange, Gem had an equal number of $10-notes and $20-notes.
4 u - 12 = 1 u + 24
4 u - 1 u = 24 + 12
3 u = 36
1 u = 36 ÷ 3 = 12
Number of $10-notes at first
= 1 u
= 12
Value of $10-notes at first
= 12 x 10
= $120
Number of $20-notes at first
= 4 u
= 4 x 12
= 48
Value of $20-notes at first
= 48 x 20
= $960
Total value of $10-notes and $20-notes at first
= 120 + 960
= $1080
Answer(s): $1080
