Sarah had a total of 54 pieces of $10 and $5 notes at first. She spent
25 of the number of $10 notes and received another 2 pieces of $5 notes from her mother. After that, the number of $5 notes she had was
12 of the remaining notes. How much money did Sarah have at first?
|
$10 |
$5 |
Total |
Before |
5 u |
3 u - 2 |
54 |
Change |
- 2 u |
+ 2 |
|
After |
3 u |
|
|
Comparing $10-notes and $5-notes |
1x3 = 3 u |
1x3 = 3 u |
|
The number of $10-notes and $5-notes in the end is the same.
The number of $10-notes in the end is repeated. Make the number of $10-notes in the end the same. LCM of 1 and 3 is 3.
Number of notes at first
= 5 u + 3 u - 2
= 8 u - 2
8 u - 2 = 54
8 u = 54 + 2
8 u = 56
1 u = 56 ÷ 8 = 7
Number of $10-notes at first
= 5 u
= 5 x 7
= 35
Total value of $10-notes at first
= 35 x 10
= $350
Number of $5-notes at first
= 3 u - 2
= 3 x 7 - 2
= 21 - 2
= 19
Total value of $5-notes at first
= 19 x 5
= $95
Amount that Sarah had at first
= 350 + 95
= $445
Answer(s): $445