The ratio of the number of $2-notes to $10-notes in Rachel's bag was 1 : 7. Rachel exchanged 9 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 Rachel's bag at first?
|
$2-notes |
$10-notes |
Before |
1 u |
7 u |
Change |
+ 45 |
- 9 |
After |
1 u + 45 |
7 u - 9 |
Value of 9 pieces of $10-notes
= 9 x 10
= $90
Number of $2-notes that Rachel exchanged for
= 90 ÷ 2
= 45
After the exchange, Rachel had an equal number of $2-notes and $10-notes.
7 u - 9 = 1 u + 45
7 u - 1 u = 45 + 9
6 u = 54
1 u = 54 ÷ 6 = 9
Number of $2-notes at first
= 1 u
= 9
Value of $2-notes at first
= 9 x 2
= $18
Number of $10-notes at first
= 7 u
= 7 x 9
= 63
Value of $10-notes at first
= 63 x 10
= $630
Total value of $2-notes and $10-notes at first
= 18 + 630
= $648
Answer(s): $648