The ratio of the number of $5-notes to $50-notes in Olivia's wallet was 1 : 8. Olivia exchanged 7 pieces of $50-notes for $5-notes. She then had an equal number of $5-notes and $50-notes. What was the total value of $5-notes and $50-notes in Olivia's wallet at first?
| |
$5-notes |
$50-notes |
| Before |
1 u |
8 u |
| Change |
+ 70 |
- 7 |
| After |
1 u + 70 |
8 u - 7 |
Value of 7 pieces of $50-notes
= 7 x 50
= $350
Number of $5-notes that Olivia exchanged for
= 350 ÷ 5
= 70
After the exchange, Olivia had an equal number of $5-notes and $50-notes.
8 u - 7 = 1 u + 70
8 u - 1 u = 70 + 7
7 u = 77
1 u = 77 ÷ 7 = 11
Number of $5-notes at first
= 1 u
= 11
Value of $5-notes at first
= 11 x 5
= $55
Number of $50-notes at first
= 8 u
= 8 x 11
= 88
Value of $50-notes at first
= 88 x 50
= $4400
Total value of $5-notes and $50-notes at first
= 55 + 4400
= $4455
Answer(s): $4455
