The ratio of the number of $2-notes to $10-notes in Olivia's handbag was 1 : 3. Olivia exchanged 4 pieces of $10-notes for $2-notes. She then had an equal number of $2-notes and $10-notes. What was the total value of $2-notes and $10-notes in Olivia's handbag at first?
|
$2-notes |
$10-notes |
Before |
1 u |
3 u |
Change |
+ 20 |
- 4 |
After |
1 u + 20 |
3 u - 4 |
Value of 4 pieces of $10-notes
= 4 x 10
= $40
Number of $2-notes that Olivia exchanged for
= 40 ÷ 2
= 20
After the exchange, Olivia had an equal number of $2-notes and $10-notes.
3 u - 4 = 1 u + 20
3 u - 1 u = 20 + 4
2 u = 24
1 u = 24 ÷ 2 = 12
Number of $2-notes at first
= 1 u
= 12
Value of $2-notes at first
= 12 x 2
= $24
Number of $10-notes at first
= 3 u
= 3 x 12
= 36
Value of $10-notes at first
= 36 x 10
= $360
Total value of $2-notes and $10-notes at first
= 24 + 360
= $384
Answer(s): $384