The sum of two numbers is 70. When the smaller number is subtracted from the bigger number, the result is 24. Find the numbers.
47 and 23
To find the numbers, let's assign variables:
Let's call the larger number "x" and the smaller number "y".
Given the problem, we have two pieces of information:
1) The sum of two numbers is 70, which can be represented as: x + y = 70.
2) When the smaller number is subtracted from the larger number, the result is 24, which can be represented as: x - y = 24.
Now we have a system of two equations:
Equation 1: x + y = 70
Equation 2: x - y = 24
There are different methods to solve this system of equations, but let's use the elimination method.
To eliminate the variable "y", we can add Equation 1 and Equation 2 to get:
(x + y) + (x - y) = 70 + 24
2x = 94
Dividing both sides of the equation by 2 gives:
x = 47.
Now that we know x = 47, we can substitute this value into one of the original equations to solve for y.
Using Equation 1:
47 + y = 70
y = 70 - 47
y = 23.
So the two numbers are x = 47 and y = 23.