Emma had a total of 49 pieces of $20 and $50 notes at first. She spent
25 of the number of $20 notes and received another 7 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 Emma have at first?
|
$20 |
$50 |
Total |
Before |
5 u |
3 u - 7 |
49 |
Change |
- 2 u |
+ 7 |
|
After |
3 u |
|
|
Comparing $20-notes and $50-notes |
1x3 = 3 u |
1x3 = 3 u |
|
The number of $20-notes and $50-notes in the end is the same.
The number of $20-notes in the end is repeated. Make the number of $20-notes in the end the same. LCM of 1 and 3 is 3.
Number of notes at first
= 5 u + 3 u - 7
= 8 u - 7
8 u - 7 = 49
8 u = 49 + 7
8 u = 56
1 u = 56 ÷ 8 = 7
Number of $20-notes at first
= 5 u
= 5 x 7
= 35
Total value of $20-notes at first
= 35 x 20
= $700
Number of $50-notes at first
= 3 u - 7
= 3 x 7 - 7
= 21 - 7
= 14
Total value of $50-notes at first
= 14 x 50
= $700
Amount that Emma had at first
= 700 + 700
= $1400
Answer(s): $1400