Elyse had a total of 87 pieces of $2 and $50 notes at first. She spent
57 of the number of $2 notes and received another 12 pieces of $50 notes from her mother. After that, the number of $50 notes she had was
12 of the remaining notes. How much money did Elyse have at first?
|
$2 |
$50 |
Total |
Before |
7 u |
2 u - 12 |
87 |
Change |
- 5 u |
+ 12 |
|
After |
2 u |
|
|
Comparing $2-notes and $50-notes |
1x2 = 2 u |
1x2 = 2 u |
|
The number of $2-notes and $50-notes in the end is the same.
The number of $2-notes in the end is repeated. Make the number of $2-notes in the end the same. LCM of 1 and 2 is 2.
Number of notes at first
= 7 u + 2 u - 12
= 9 u - 12
9 u - 12 = 87
9 u = 87 + 12
9 u = 99
1 u = 99 ÷ 9 = 11
Number of $2-notes at first
= 7 u
= 7 x 11
= 77
Total value of $2-notes at first
= 77 x 2
= $154
Number of $50-notes at first
= 2 u - 12
= 2 x 11 - 12
= 22 - 12
= 10
Total value of $50-notes at first
= 10 x 50
= $500
Amount that Elyse had at first
= 154 + 500
= $654
Answer(s): $654