Yen had a total of 54 pieces of $50 and $20 notes at first. She spent
35 of the number of $50 notes and received another 2 pieces of $20 notes from her mother. After that, the number of $20 notes she had was
12 of the remaining notes. How much money did Yen have at first?
|
$50 |
$20 |
Total |
Before |
5 u |
2 u - 2 |
54 |
Change |
- 3 u |
+ 2 |
|
After |
2 u |
|
|
Comparing $50-notes and $20-notes |
1x2 = 2 u |
1x2 = 2 u |
|
The number of $50-notes and $20-notes in the end is the same.
The number of $50-notes in the end is repeated. Make the number of $50-notes in the end the same. LCM of 1 and 2 is 2.
Number of notes at first
= 5 u + 2 u - 2
= 7 u - 2
7 u - 2 = 54
7 u = 54 + 2
7 u = 56
1 u = 56 ÷ 7 = 8
Number of $50-notes at first
= 5 u
= 5 x 8
= 40
Total value of $50-notes at first
= 40 x 50
= $2000
Number of $20-notes at first
= 2 u - 2
= 2 x 8 - 2
= 16 - 2
= 14
Total value of $20-notes at first
= 14 x 20
= $280
Amount that Yen had at first
= 2000 + 280
= $2280
Answer(s): $2280