The ratio of the number of $2-notes to $10-notes in Esther's jar was 1 : 3. Esther exchanged 12 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 Esther's jar at first?
|
$2-notes |
$10-notes |
Before |
1 u |
3 u |
Change |
+ 60 |
- 12 |
After |
1 u + 60 |
3 u - 12 |
Value of 12 pieces of $10-notes
= 12 x 10
= $120
Number of $2-notes that Esther exchanged for
= 120 ÷ 2
= 60
After the exchange, Esther had an equal number of $2-notes and $10-notes.
3 u - 12 = 1 u + 60
3 u - 1 u = 60 + 12
2 u = 72
1 u = 72 ÷ 2 = 36
Number of $2-notes at first
= 1 u
= 36
Value of $2-notes at first
= 36 x 2
= $72
Number of $10-notes at first
= 3 u
= 3 x 36
= 108
Value of $10-notes at first
= 108 x 10
= $1080
Total value of $2-notes and $10-notes at first
= 72 + 1080
= $1152
Answer(s): $1152