Nitya and satya have some marbles with them. Nitya says to Satya, "If you give one marble to me, we will have equal number of marbles." Satya says to Nitya," If you give me one marble, I will have twice the number of marbles you have". How many marbles to.Nitya and Satya have respectively?
Please help!!!
To solve this problem, let's assume that Nitya has x number of marbles and Satya has y number of marbles.
According to the first statement, if Satya gives one marble to Nitya, they will have an equal number of marbles. This can be written as:
x + 1 = y - 1 Equation 1
By simplifying Equation 1, we get:
x - y = -2 Equation 2
According to the second statement, if Nitya gives one marble to Satya, Satya will have twice the number of marbles Nitya has. This can be written as:
x - 1 = 2(y + 1) Equation 3
By simplifying Equation 3, we get:
x - 1 = 2y + 2 Equation 4
Now, we have two equations (Equations 2 and 4) with two unknowns (x and y). We can solve this system of equations to find the values of x and y.
Let's solve Equations 2 and 4 by the method of substitution:
From Equation 2, we can express x in terms of y:
x = -2 + y
Now, substitute this expression for x in Equation 4:
(-2 + y) - 1 = 2y + 2
Simplifying this equation, we get:
-3 + y = 2y + 2
Subtracting y from both sides:
-3 = y + 2
Subtracting 2 from both sides:
-5 = y
Now, substitute this value of y in Equation 2 to find x:
x = -2 + (-5)
x = -2 - 5
x = -7
Therefore, Nitya has -7 marbles and Satya has -5 marbles.
However, it's not possible to have negative marbles as the number of marbles cannot be negative. Therefore, there is no solution to this problem.
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