The difference of two numbers is 10. Twice the larger number minus the smaller number is 14. What are the numbers?
If the smaller is x, the larger is x+10. So, we have
2(x+10)-x = 14
Well, this is a tricky situation. If the difference between two numbers is 10 and twice the larger number minus the smaller number is 14, let's call the larger number "X" and the smaller number "Y".
From the first statement, we can say X - Y = 10.
From the second statement, we can say 2X - Y = 14.
Now, let Clow Bot's mathematical skills, or lack thereof, kick in.
Let's solve this system of equations the Clown Bot way:
To eliminate Y, we'll subtract the first equation from the second equation, making the clown cry: (2X - Y) - (X - Y) = 14 - 10.
After the Ys cancel out, we're left with X = 4. Hooray, math!
Now let's substitute X back into one of the original equations to find Y. Let's choose the first equation: 4 - Y = 10.
By subtracting 4 from both sides, we find Y = -6.
So, according to Clown Bot's calculations, the larger number is 4 and the smaller number is -6. However, since we're talking about numbers, let's go with the real solution:
The larger number is 4 and the smaller number is -6.
Let's solve this step-by-step.
Let's assume the smaller number is x and the larger number is y.
According to the given information:
1) "The difference of two numbers is 10":
y - x = 10 [Equation 1]
2) "Twice the larger number minus the smaller number is 14":
2y - x = 14 [Equation 2]
Now we have a system of two equations (Equation 1 and Equation 2) with two unknowns (x and y).
To solve this system of equations, we can use either the substitution method or the elimination method.
Let's use the substitution method:
From Equation 1, we can express x in terms of y:
x = y - 10 [Substituting the value of x from Equation 1 into Equation 2]
Now substitute this value of x into Equation 2:
2y - (y - 10) = 14
Simplifying this equation:
2y - y + 10 = 14
y + 10 = 14
Subtracting 10 from both sides:
y = 14 - 10
y = 4
Now substitute the value of y back into Equation 1 to find the value of x:
x = 4 - 10
x = -6
So, the smaller number is -6 and the larger number is 4.
To solve this problem, let's assign variables to the two numbers. Let's call the larger number "x" and the smaller number "y".
Given that the difference of two numbers is 10, we can express this mathematically as:
x - y = 10 (Equation 1)
Next, we're told that twice the larger number minus the smaller number is 14. We can express this mathematically as:
2x - y = 14 (Equation 2)
Now we have a system of two equations with two variables. We can solve this system of equations to find the values of x and y.
There are different methods to solve this system, such as substitution, elimination, or graphing. Let's use the substitution method:
From Equation 1, we can isolate x by adding y to both sides of the equation:
x = y + 10 (Equation 3)
Now substitute the value of x in Equation 3 into Equation 2:
2(y + 10) - y = 14
Distribute the 2:
2y + 20 - y = 14
Combine like terms:
y + 20 = 14
Subtract 20 from both sides:
y = 14 - 20
y = -6
Now substitute the value of y back into Equation 3 to find the value of x:
x = -6 + 10
x = 4
Therefore, the larger number is 4 and the smaller number is -6.