Barbara had a total of 70 pieces of $2 and $20 notes at first. She spent
58 of the number of $2 notes and received another 7 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 Barbara have at first?
|
$2 |
$20 |
Total |
Before |
8 u |
3 u - 7 |
70 |
Change |
- 5 u |
+ 7 |
|
After |
3 u |
|
|
Comparing $2-notes and $20-notes |
1x3 = 3 u |
1x3 = 3 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 3 is 3.
Number of notes at first
= 8 u + 3 u - 7
= 11 u - 7
11 u - 7 = 70
11 u = 70 + 7
11 u = 77
1 u = 77 ÷ 11 = 7
Number of $2-notes at first
= 8 u
= 8 x 7
= 56
Total value of $2-notes at first
= 56 x 2
= $112
Number of $20-notes at first
= 3 u - 7
= 3 x 7 - 7
= 21 - 7
= 14
Total value of $20-notes at first
= 14 x 20
= $280
Amount that Barbara had at first
= 112 + 280
= $392
Answer(s): $392