Cathy had a total of 55 pieces of $2 and $20 notes at first. She spent
27 of the number of $2 notes and received another 5 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 Cathy have at first?
|
$2 |
$20 |
Total |
Before |
7 u |
5 u - 5 |
55 |
Change |
- 2 u |
+ 5 |
|
After |
5 u |
|
|
Comparing $2-notes and $20-notes |
1x5 = 5 u |
1x5 = 5 u |
|
The number of $2-notes and $20-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 5 is 5.
Number of notes at first
= 7 u + 5 u - 5
= 12 u - 5
12 u - 5 = 55
12 u = 55 + 5
12 u = 60
1 u = 60 ÷ 12 = 5
Number of $2-notes at first
= 7 u
= 7 x 5
= 35
Total value of $2-notes at first
= 35 x 2
= $70
Number of $20-notes at first
= 5 u - 5
= 5 x 5 - 5
= 25 - 5
= 20
Total value of $20-notes at first
= 20 x 20
= $400
Amount that Cathy had at first
= 70 + 400
= $470
Answer(s): $470