help me for this sum?

2009-05-16 9:56 am
It was vacation time, & so I decided to visit my cousin’s house. What a grand time we had! In the mornings, we both would go for a jog; the evenings were spent on a tennis court. Tiring as these activities were, we could manage 1 per day, i. e., either we went for a jog or played tennis. There were days when we felt lazy and stayed home all day long. Now, there were 12 mornings when we did nothing, 17 evenings when we stayed at home, and a total of 11 days when we jogged or played tennis. For how many days did I stay at my cousin’s place?

回答 (3)

2009-05-16 11:48 am
✔ 最佳答案
It seems to be a bit clumsy but the question itself is just a bit of equation. The key to the solution is "how to organize the info in a SYSTEMATIC way & transcribe a lump of words into mathematical expressions". That's what I'm trying to demonstrate.

[Variables] (minimizing no. of variables)
Let N be the total no. of days of stay (i.e. the target answer);
and J be the no. of mornings spent on jogging,
(11-J) be the no. of evenings spent on tennis.

[Illustration] (listing out known situations & relationships: the MOST important part yet often badly done)
The possible situations of spending 1 day are:
. . . . . . . . . .(i) . . . .(ii) . . . . .(iii)
1. morning . idle . jogging(J) . idle
2. evening . .idle . . idle . . . .tennis(11-J)

Other known info:
No. of idle ...
- 3. mornings: 12
- 4. evenings : 17
No. of mornings = N
No. of evenings = N (quite silly though...)

[Equations] (finally... constructing equations using the established info)
Based on 1 & 3, we have: N - J = 12
Based on 2 & 4, we have: N - (11-J) = 17

Solving the simultaneous equations,
N = 20; J = 8

Therefore, the stay is 20 days.

* * *
Hope you don't find it boring reading such a long answer.
Please notify me if you also want the steps for solving the equations above.
2009-05-17 6:55 pm
20 days
2009-05-16 7:05 pm
20 days

3 evening for tennis
8 morning for jogging


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