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We would like to share equally a sum of money between multiple people. If we give 20$ to each person there will be 40$ left over.
If we give 25$ to each person there will be 75$ short off. How many people are there?
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Let N be the number of people, and let M be an amount of money (in dollars).
The condition says
M = 20*N + 40 (1) ("If we give 20$ to each person there will be 40$ left over.")
The condition also says
M = 25*N - 75 (2) ("If we give 25$ to each person there will be 75$ short off.")
Left sides of equations (1) and (2) are the same. Hence, their right sides are equal:
20*N + 40 = 25*N - 75. (3)
It is your key/major equation. Solve it to find N:
40 + 75 = 25N - 20N ====> 5N = 115 ====> N = = 23.
There were 23 people and M = 20*N + 40 = 20*23 + 40 = 500 dollars.
Check. 23*20 = 460 dollars, and 40 dollars left.
23*25 = 575 dollars, and 75 dollars short off.
Answer. There were 23 people and 500 dollars.
Their wording was not perfect (in my view), so I edited it, according to my common sense.
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If you want to see more similar problems solved, look in my lesson
- Had they sold . . .
in this site.
Happy learning ! !