The sum of two numbers is 73. Their difference is 21. Find the larger number.?
x+y = 73
x-y = 21
add them
2x = 94
x = 47
sub into the firs
47+y = 73
y = 26
check: 47+26 = 73 and 47-26 = 21
YEahhh!
Well, this sounds like a job for the Math Police! Don't worry, I'll crack the case for you. Let's say the larger number is x, and the smaller number is y. We know that x + y = 73, and x - y = 21.
To solve this mystery, we can use some detective work called elimination. By adding the two equations together, we can eliminate one of the variables. Let's do some quick math here. (x + y) + (x - y) = 73 + 21.
After some intense adding and subtracting, we find that 2x = 94. If we divide both sides by 2, we discover that x = 47.
So, the larger number in this mysterious case is 47! Case solved!
Step 1: Let's start by assigning variables to the two unknown numbers. Let's call the larger number 'x' and the smaller number 'y'.
Step 2: We know that the sum of the two numbers is 73. So, we can write the equation as:
x + y = 73 (Equation 1)
Step 3: We also know that the difference between the two numbers is 21. So, we can write another equation as:
x - y = 21 (Equation 2)
Step 4: Now we have a system of two equations with two variables. We can solve this system of equations by using the method of substitution or elimination.
Step 5: Let's solve it using the substitution method. Solve equation 2 for x:
x = y + 21 (Equation 3)
Step 6: Substitute equation 3 into equation 1:
(y + 21) + y = 73
Step 7: Simplify the equation:
2y + 21 = 73
Step 8: Subtract 21 from both sides of the equation to isolate the variable:
2y = 73 - 21
= 52
Step 9: Divide both sides by 2 to solve for y:
y = 52 / 2
= 26
Step 10: We have found the value of the smaller number, which is y = 26. To find the larger number, substitute this value back into equation 3:
x = y + 21
= 26 + 21
= 47
Step 11: Therefore, the larger number is 47.
To find the larger number, we'll need to set up a system of equations based on the given information.
Let's assume the larger number is x and the smaller number is y.
We know that the sum of two numbers is 73, so our first equation is:
x + y = 73
We also know that their difference is 21, so our second equation is:
x - y = 21
To solve this system of equations, we can use the method of substitution or the method of elimination.
Method of substitution:
1. Solve one equation for one variable in terms of the other variable. Let's solve the first equation for x:
x = 73 - y
2. Substitute the expression for x in the second equation:
73 - y - y = 21
3. Simplify the equation:
73 - 2y = 21
4. Move the constant to the other side of the equation:
-2y = 21 - 73
5. Simplify:
-2y = -52
6. Divide both sides of the equation by -2:
y = 26
7. Substitute the value of y back into the first equation:
x + 26 = 73
8. Solve for x:
x = 73 - 26
9. Simplify:
x = 47
Therefore, the larger number is 47.