The ratio of the number of $5-notes to $10-notes in Emma's handbag was 1 : 4. Emma exchanged 10 pieces of $10-notes for $5-notes. She then had an equal number of $5-notes and $10-notes. What was the total value of $5-notes and $10-notes in Emma's handbag at first?
| |
$5-notes |
$10-notes |
| Before |
1 u |
4 u |
| Change |
+ 20 |
- 10 |
| After |
1 u + 20 |
4 u - 10 |
Value of 10 pieces of $10-notes
= 10 x 10
= $100
Number of $5-notes that Emma exchanged for
= 100 ÷ 5
= 20
After the exchange, Emma had an equal number of $5-notes and $10-notes.
4 u - 10 = 1 u + 20
4 u - 1 u = 20 + 10
3 u = 30
1 u = 30 ÷ 3 = 10
Number of $5-notes at first
= 1 u
= 10
Value of $5-notes at first
= 10 x 5
= $50
Number of $10-notes at first
= 4 u
= 4 x 10
= 40
Value of $10-notes at first
= 40 x 10
= $400
Total value of $5-notes and $10-notes at first
= 50 + 400
= $450
Answer(s): $450
