The number of sweets in Container X was 24 more than Container Y. When I removed 42 sweets from Container X and transfered then in Container Y,the number of sweets in Container Y became thrice of Container X. Find the number of sweets in Container X first.
x = The number of sweets in container x
y = The number of sweets in Container y
x = 24 + y
OR
y = x - 24
When you removed 42 sweets from container x then numers of sweets in container x became: x - 42
Numbers of sweets in container y became: y + 42 = thrice of ( x - 42 ) = 3 ( x - 42 )
y + 42 = 3 ( x - 42 )
Remark : y = x - 24
( x - 24 ) + 42 = 3 ( x - 42 )
x - 24 + 42 = 3 * x - 3 * 42
x + 18 = 3 x - 126
18 + 126 = 3 x - x
144 = 2 x
2 x = 144 Divide both sides by 2
x = 144 / 2
x = 72
y = x - 24
y = 72 - 24
y = 48
Cheking :
x - 42 = 72 - 42 = 30
y + 42 = 48 + 42 = 90
90 / 30 = 3
Let's solve this step by step.
Let's assume the number of sweets in Container Y as 'Y'.
According to the given information, the number of sweets in Container X is 24 more than Container Y. So the number of sweets in Container X can be expressed as 'Y + 24'.
Now, when 42 sweets are removed from Container X and transferred to Container Y, the number of sweets in Container Y becomes thrice of Container X. This can be expressed as 'Y + 42 = 3(Y + 24)'.
Let's solve this equation step by step:
Expanding the equation:
Y + 42 = 3Y + 72
Combining like terms:
-2Y = -30
Dividing by -2:
Y = 15
So, the number of sweets in Container Y is 15.
Now, we can find the number of sweets in Container X by using the previously derived equation:
X = Y + 24
X = 15 + 24
X = 39
Therefore, the number of sweets in Container X is 39.
To solve this problem, let's break it down step by step:
Step 1: Set up the equations:
Let's assume the number of sweets in Container X is "X", and the number of sweets in Container Y is "Y".
According to the given information, the number of sweets in Container X (X) is 24 more than the number of sweets in Container Y (Y).
So, we can set up the equation: X = Y + 24. Equation 1
After removing 42 sweets from Container X and transferring them to Container Y, the number of sweets in Container Y became three times the number of sweets in Container X.
So, the equation becomes: Y + 42 = 3(X - 42) Equation 2
Step 2: Solve the equations simultaneously:
We can solve the equations by substituting the value of X from Equation 1 into Equation 2.
Substituting X = Y + 24 in Equation 2:
Y + 42 = 3((Y + 24) - 42)
Simplifying the equation:
Y + 42 = 3(Y - 18)
Expanding the equation:
Y + 42 = 3Y - 54
Combining like terms:
42 + 54 = 3Y - Y
96 = 2Y
Dividing both sides by 2:
48 = Y
Step 3: Calculate the number of sweets in Container X:
We can substitute the value of Y in Equation 1 to solve for X:
X = Y + 24
X = 48 + 24
X = 72
Therefore, the initial number of sweets in Container X is 72.