Pamela and Asher collect pencils and erasers. Asher has 44 less pencils than erasers. Asher has 2 times the number of pencils Pamela has, and Pamela has 25% more erasers than Asher. After Pamela gives Asher all of her pencils and Asher gives Pamela 75% of his erasers, Asher has 39 less erasers than pencils. Find the number of erasers Pamela has at first.
Pamela |
Asher |
Erasers |
Pencils |
Erasers |
Pencils |
2.5 u + 55 |
1 u |
2 u + 44 |
2 u |
+ 1.5 u + 33 |
- 1 u |
- 1.5 u - 33 |
+ 1 u |
4 u + 88 |
0 |
0.5 u + 11 |
3 u |
100%+ 25% = 125%
125% x 2 u
=
125100 x 2 u
= 2.5 u
125% x 44
=
125100 x 44
= 55
75% x 2 u
=
75100 x 2 u
= 1.5 u
75% x 44
=
75100 x 44
= 33
If another 39 erasers are given to Asher, he will have equal number of erasers and pencils in the end.
3 u = 0.5 u + 11 + 39
3 u - 0.5 u = 50
2.5 u = 50
1 u = 50 ÷ 2.5 = 20
Number of erasers that Pamela has at first
= 2.5 u + 55
= 2.5 x 20 + 55
= 50 + 55
= 105
Answer(s): 105