Emma and Ahmad collect cards and pens. Ahmad has 100 less cards than pens. Ahmad has 5 times the number of cards Emma has, and Emma has 25% more pens than Ahmad. After Emma gives Ahmad all of her cards and Ahmad gives Emma 75% of his pens, Ahmad has 51 less pens than cards. Find the number of pens Emma has at first.
Emma |
Ahmad |
Pens |
Cards |
Pens |
Cards |
6.25 u + 125 |
1 u |
5 u + 100 |
5 u |
+ 3.75 u + 75 |
- 1 u |
- 3.75 u - 75 |
+ 1 u |
10 u + 200 |
0 |
1.25 u + 25 |
6 u |
100%+ 25% = 125%
125% x 5 u
=
125100 x 5 u
= 6.25 u
125% x 100
=
125100 x 100
= 125
75% x 5 u
=
75100 x 5 u
= 3.75 u
75% x 100
=
75100 x 100
= 75
If another 51 pens are given to Ahmad, he will have equal number of pens and cards in the end.
6 u = 1.25 u + 25 + 51
6 u - 1.25 u = 76
4.75 u = 76
1 u = 76 ÷ 4.75 = 16
Number of pens that Emma has at first
= 6.25 u + 125
= 6.25 x 16 + 125
= 100 + 125
= 225
Answer(s): 225