There was an equal number of chairs and benches in the morning. At 2 p.m., some chairs were added and some benches were removed, resulting in the number of chairs being increased by 20% while the number of benches decreased by 30%. At 5 p.m. the number of chairs increased by 50%. If a total of 80 chairs were added during the day, how many more chairs than benches were there in the end?
At 2 p.m. |
Chairs |
Benches |
Before |
1 u |
1 u |
Change |
+ 0.2 u |
- 0.3 u |
After |
1.2 u |
0.7 u |
At 5 p.m. |
Chairs |
Benches |
Before |
1.2 u |
0.7 u |
Change |
+ 0.6 u |
No change |
After |
1.8 u |
0.7 u |
Number of chairs added
= 20% x 1 u
=
20100 x 1 u
= 0.2 u
Number of benches removed
= 30% x 1 u
=
30100 x 1 u
= 0.3 u
Number of chairs increased by chairs at 5 p.m.
= 50% x 1.2 u
=
50100 x 1.2 u
= 0.6 u
Number of chairs added during the day
= 1.8 u - 1 u
= 0.8 u
0.8 u = 80
1 u = 80 ÷ 0.8 = 100
Number of more chairs than benches in the end
= 1.8 u - 0.7 u
= 1.1 u
= 1.1 x 100
= 110
Answer(s): 110