Gem had a total of 19 pieces of $10 and $20 notes at first. She spent
47 of the number of $10 notes and received another 11 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 Gem have at first?
|
$10 |
$20 |
Total |
Before |
7 u |
3 u - 11 |
19 |
Change |
- 4 u |
+ 11 |
|
After |
3 u |
|
|
Comparing $10-notes and $20-notes |
1x3 = 3 u |
1x3 = 3 u |
|
The number of $10-notes and $20-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 - 11
= 10 u - 11
10 u - 11 = 19
10 u = 19 + 11
10 u = 30
1 u = 30 ÷ 10 = 3
Number of $10-notes at first
= 7 u
= 7 x 3
= 21
Total value of $10-notes at first
= 21 x 10
= $210
Number of $20-notes at first
= 3 u - 11
= 3 x 3 - 11
= 9 - 11
= -2
Total value of $20-notes at first
= -2 x 20
= $-40
Amount that Gem had at first
= 210 + -40
= $170
Answer(s): $170