The sum of two numbers is 32. Ten more than half of the sum of the numbers is 26. What are the numbers?
Solve these two simultaneous equations, for the unknowns x and y.
x + y = 32
(x + y)/2 + 10 = 26
The second equation reduces to x + y = 32 also.
The two equations are not independent. Any pair of numbers that add up to 32 will work.
5 And4
To solve this problem, let's assign variables to represent the unknown numbers. Let's call the first number x and the second number y. We can translate the given information into equations.
1. "The sum of two numbers is 32" can be written as:
x + y = 32
2. "Ten more than half of the sum of the numbers is 26" can be written as:
0.5(x + y) + 10 = 26
Now, we have a system of two equations. We can use substitution or elimination method to solve for x and y.
Let's use substitution method:
1. Rearrange the first equation to solve for x:
x = 32 - y
2. Substitute this expression for x in the second equation:
0.5(32 - y + y) + 10 = 26
Simplifying further:
16 - 0.5y + 10 = 26
-0.5y + 26 = 26 - 16
-0.5y = 10
y = 10 / -0.5
y = -20
3. Substitute the value of y (-20) back into the first equation to solve for x:
x + (-20) = 32
x - 20 = 32
x = 32 + 20
x = 52
Therefore, the two numbers are x = 52 and y = -20.