Mr Tan has some amount of money. If he distributes equally to 2 persons, he left with $1.If he distributes equally to 3 persons, he left with $2.If he distributes equally to 4 persons, he left with $3.If he distributes equally to 5 persons, he left with $4.If he distributes equally to 6 persons, he left with $5.If he distributes equally to 7 persons, he left with $6.If he distributes equally to 8 persons, he left with $7.If he distributes equally to 9 persons, he left with $8.If he distributes equally to 10 persons, he left with $9.Find what is the amount of money does Mr Tan have?
To find the amount of money Mr. Tan has, we can use a method called algebraic reasoning. Let's assign a variable to represent the unknown amount of money Mr. Tan has. Let's call this variable "x".
According to the information given, we can set up a series of equations based on the given conditions:
1) If Mr. Tan distributes the money equally to 2 persons, he is left with $1:
x - (2 * 1) = 1
2) If Mr. Tan distributes the money equally to 3 persons, he is left with $2:
x - (3 * 2) = 2
3) If Mr. Tan distributes the money equally to 4 persons, he is left with $3:
x - (4 * 3) = 3
And so on...
We can continue setting up equations for the remaining conditions:
4) x - (5 * 4) = 4
5) x - (6 * 5) = 5
6) x - (7 * 6) = 6
7) x - (8 * 7) = 7
8) x - (9 * 8) = 8
9) x - (10 * 9) = 9
Now, let's solve this system of equations to find the value of "x".
By simplifying each equation, we get:
1) x - 2 = 1
2) x - 6 = 2
3) x - 12 = 3
4) x - 20 = 4
5) x - 30 = 5
6) x - 42 = 6
7) x - 56 = 7
8) x - 72 = 8
9) x - 90 = 9
Simplifying each equation further by adding the constant value on the right side to both sides of the equation, we get:
1) x = 3
2) x = 8
3) x = 15
4) x = 24
5) x = 35
6) x = 48
7) x = 63
8) x = 80
9) x = 99
From these solutions, we can see that the value of "x" that satisfies all the equations is 99. Therefore, Mr. Tan has $99.