Jean had 4 times as many erasers as pens. After she used 105 erasers and 7 pens, there were twice as many pens as erasers.
- How many erasers did Jean have in the end?
- How many pens did Jean have at first?
| |
Erasers |
Pens |
Comparing erasers
and pens at first |
4 p
|
1 p
|
| Before |
1 u + 105 |
2 u + 7 |
| Change |
- 105 |
- 7 |
| After |
1 u |
2 u |
(a)
1 u + 105 = 4 p --- (1)
2 u + 7 = 1 p --- (2)
(2)
x 4
8 u + 28 = 4 p ---(3)
(3) = (1)
8 u + 28 = 1 u + 105
8 u - 1 u = 105 - 28
7 u = 77
1 u = 77 ÷ 7 = 11
Number of erasers that Jean had in the end
= 1 u
= 11
(b)
Number of pens that Jean had at first
= 2 u + 7
= 2 x 11 + 7
= 22 + 7
= 29
Answer(s): (a) 11; (b) 29
