Gabby had 3 times as many erasers as cards. After she used 71 erasers and 7 cards, there were twice as many cards as erasers.
- How many erasers did Gabby have in the end?
- How many cards did Gabby have at first?
| |
Erasers |
Cards |
Comparing erasers
and cards at first |
3 p
|
1 p
|
| Before |
1 u + 71 |
2 u + 7 |
| Change |
- 71 |
- 7 |
| After |
1 u |
2 u |
(a)
1 u + 71 = 3 p --- (1)
2 u + 7 = 1 p --- (2)
(2)
x 3
6 u + 21 = 3 p ---(3)
(3) = (1)
6 u + 21 = 1 u + 71
6 u - 1 u = 71 - 21
5 u = 50
1 u = 50 ÷ 5 = 10
Number of erasers that Gabby had in the end
= 1 u
= 10
(b)
Number of cards that Gabby had at first
= 2 u + 7
= 2 x 10 + 7
= 20 + 7
= 27
Answer(s): (a) 10; (b) 27
