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An amount of money was divided between some people in such a way that if there had been 4 more people, everyone would have got $16 less. But if there had been 4 less people, everyone would got $24 more. How many people were there in the group?
How could I solve this?
1. LetQuote:
Originally Posted by geton
x denote the number of people in the group;
y denote the amount of money each person will get.
2. "Translate" the text into equations:
3. Expand the brackets and subtract the 1st equation columnwise from the 2nd equation. After moving some stuff around you'll get:
----- [A]
4. Substitute in the 1st equation the variable y by 5x - 4. Expand the brackets and solve for x.
5. Plug in the value of x into the equato [A] to calculate y.
6.
Spoiler:
Thank you so much :)Quote:
Originally Posted by earboth1. Let
x denote the number of people in the group;
y denote the amount of money each person will get.
2. "Translate" the text into equations:
3. Expand the brackets and subtract the 1st equation columnwise from the 2nd equation. After moving some stuff around you'll get:
4. Substitute in the 1st equation the variable y by 5x - 4. Expand the brackets and solve for x.
5. Plug in the value of x into the equato [A] to calculate y.
6.
Spoiler:
Alternatively, the sum of money is constant, while the number of people and each one's share varies.Quote:
Originally Posted by geton
The number of people multiplied by each one's share always equals the sum of money.
number of people;
each one's share.
We requireonly, so subtract
from all three expressions...
Add these to eliminateas both are zero...