The sum of two numbers is 68 and the difference is 10. What are the numbers?
x + y = 68
x - y = 10
Add the two equations.
2x = 78
Insert the value of x into the first equation and solve for y. Check by inserting both values into the second equation.
Well, well, well, looks like we have a classic case of number mischief! Let me don my clown hat and juggle some numbers for you.
So, let's call one of those sneaky numbers x and the other one y. If their sum is 68, we can write an equation like this: x + y = 68.
And if their difference is 10, we can put another equation to the test: x - y = 10.
Now, let's see what kind of clown magic we can conjure up with these equations.
If we add these two equations together, the y's will conveniently cancel each other out, leaving us with 2x = 78. Divide both sides by 2, and voila! We find that x = 39.
Now if we subtract that second equation from the first, we can isolate y: (x + y) - (x - y) = 68 - 10. Simplifying that, we get 2y = 58. Divide both sides by 2 and we get y = 29.
So, the sneaky numbers are 39 and 29. Ta-da! Clowns can do math too! 🎉
Let's assume the first number is 'x' and the second number is 'y'.
According to the given information:
1) The sum of the two numbers is 68, so the equation becomes: x + y = 68.
2) The difference between the two numbers is 10, so the equation becomes: x - y = 10.
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve it using the method of substitution:
1) Rearrange the equation x - y = 10 to get x = 10 + y.
2) Substitute this value of x in the first equation: 10 + y + y = 68.
3) Simplify the equation: 2y + 10 = 68.
4) Subtract 10 from both sides: 2y = 58.
5) Divide both sides by 2: y = 29.
Now, substitute the value of y back into either of the original equations to find x:
x + 29 = 68, so x = 68 - 29 = 39.
Therefore, the two numbers are 39 and 29.
To find the two numbers, we'll set up a system of equations based on the given information. Let's represent the two numbers as x and y.
From the given information, we can set up the following equations:
Equation 1: x + y = 68 (The sum of the two numbers is 68)
Equation 2: x - y = 10 (The difference between the two numbers is 10)
Now, we can solve this system of equations to find the values of x and y.
There are several ways to solve a system of equations, but one common method is the substitution method. Here's how it works:
1. Solve one equation for one variable in terms of the other variable.
We'll solve Equation 2 for x:
x = y + 10
2. Substitute the expression for the variable found in step 1 into the other equation.
Substituting x = y + 10 into Equation 1:
(y + 10) + y = 68
3. Simplify and solve for the remaining variable.
2y + 10 = 68
2y = 68 - 10
2y = 58
y = 58/2
y = 29
4. Substitute the value found in step 3 back into one of the original equations to solve for the other variable.
Using Equation 1:
x + 29 = 68
x = 68 - 29
x = 39
So, the two numbers are 39 and 29.