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All people in a village were going on a picnic using many vehicles and there were equal No. of people in each of those vehicles.
Half way down their trip, 10 vehicles broke down and they had to accomodate one person extra in each of the remaining vehicles.
while returning, 15 other vehicles broke down and the people were tranfered to the remaining vehicles equally.
Overall, there were 3 additional people in each of the remaining vehicles. How many people were there in the village?
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Let "n" be the number of people in each of "v" vehicle originally (than "n" is the same for (or "in") each vehicle,
according to the condition).
Then the total number of people is v*n, obviously. It is the total number of people in the village.
After 10 vehicles were broken, the number of remaining vehicles became (v-10), carrying (n+1) people in each.
It gives you an equation
(v-10)*(n+1) = vn.
Open parentheses, collect like terms, cancel like terms, and you will get from it
10v - v = -10. (1)
It is your first basic equation.
When next 15 vehicle were broken, the number of remaining vehicles became (v-25), carrying (n+3) people in each.
It gives you an equation
(v-10)*(n+1) = vn.
Open parentheses, collect like terms, cancel like terms, and you will get from it
25n - 3v = -75. (2)
It is your second basic equation.
Solve the two equations by any method you know. You will get n = 9 and v = 100.
So, there were v*n = 100*9 = 900 people in the village.
If you want to see similar solved problems, see the lesson
- Had they sold . . .
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Miscellaneous word problems".