There was an equal number of benches and chairs in the morning. At 2 p.m., some benches were added and some chairs were removed, resulting in the number of benches being increased by 20% while the number of chairs decreased by 40%. At 8 p.m. the number of benches increased by 50%. If a total of 52 benches were added during the day, how many more benches than chairs were there in the end?
At 2 p.m. |
Benches |
Chairs |
Before |
1 u |
1 u |
Change |
+ 0.2 u |
- 0.4 u |
After |
1.2 u |
0.6 u |
At 8 p.m. |
Benches |
Chairs |
Before |
1.2 u |
0.6 u |
Change |
+ 0.6 u |
No change |
After |
1.8 u |
0.6 u |
Number of benches added
= 20% x 1 u
=
20100 x 1 u
= 0.2 u
Number of chairs removed
= 40% x 1 u
=
40100 x 1 u
= 0.4 u
Number of benches increased by benches at 8 p.m.
= 50% x 1.2 u
=
50100 x 1.2 u
= 0.6 u
Number of benches added during the day
= 1.8 u - 1 u
= 0.8 u
0.8 u = 52
1 u = 52 ÷ 0.8 = 65
Number of more benches than chairs in the end
= 1.8 u - 0.6 u
= 1.2 u
= 1.2 x 65
= 78
Answer(s): 78