The ratio of the number of $20-notes to $50-notes in Esther's handbag was 1 : 3. Esther exchanged 8 pieces of $50-notes for $20-notes. She then had an equal number of $20-notes and $50-notes. What was the total value of $20-notes and $50-notes in Esther's handbag at first?
|
$20-notes |
$50-notes |
Before |
1 u |
3 u |
Change |
+ 20 |
- 8 |
After |
1 u + 20 |
3 u - 8 |
Value of 8 pieces of $50-notes
= 8 x 50
= $400
Number of $20-notes that Esther exchanged for
= 400 ÷ 20
= 20
After the exchange, Esther had an equal number of $20-notes and $50-notes.
3 u - 8 = 1 u + 20
3 u - 1 u = 20 + 8
2 u = 28
1 u = 28 ÷ 2 = 14
Number of $20-notes at first
= 1 u
= 14
Value of $20-notes at first
= 14 x 20
= $280
Number of $50-notes at first
= 3 u
= 3 x 14
= 42
Value of $50-notes at first
= 42 x 50
= $2100
Total value of $20-notes and $50-notes at first
= 280 + 2100
= $2380
Answer(s): $2380