Yen had a total of 58 pieces of $10 and $2 notes at first. She spent
47 of the number of $10 notes and received another 12 pieces of $2 notes from her mother. After that, the number of $2 notes she had was
12 of the remaining notes. How much money did Yen have at first?
|
$10 |
$2 |
Total |
Before |
7 u |
3 u - 12 |
58 |
Change |
- 4 u |
+ 12 |
|
After |
3 u |
|
|
Comparing $10-notes and $2-notes |
1x3 = 3 u |
1x3 = 3 u |
|
The number of $10-notes and $2-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
= 7 u + 3 u - 12
= 10 u - 12
10 u - 12 = 58
10 u = 58 + 12
10 u = 70
1 u = 70 ÷ 10 = 7
Number of $10-notes at first
= 7 u
= 7 x 7
= 49
Total value of $10-notes at first
= 49 x 10
= $490
Number of $2-notes at first
= 3 u - 12
= 3 x 7 - 12
= 21 - 12
= 9
Total value of $2-notes at first
= 9 x 2
= $18
Amount that Yen had at first
= 490 + 18
= $508
Answer(s): $508