the sum of two numbers is 87 & their difference is 35. find the numbers.
To find the two numbers, we can set up a system of equations based on the given information.
Let's assume the two numbers are x and y.
Given that the sum of the two numbers is 87, we can write the equation as:
x + y = 87 -- Equation 1
Given that the difference between the two numbers is 35, we can write the equation as:
x - y = 35 -- Equation 2
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of elimination to solve this system.
We can add Equation 1 and Equation 2 together:
(x + y) + (x - y) = 87 + 35
2x = 122
Next, we can divide both sides of the equation by 2 to isolate x:
2x/2 = 122/2
x = 61
Now that we have found the value of x, we can substitute it into Equation 1 to find y:
61 + y = 87
y = 87 - 61
y = 26
Therefore, the two numbers are 61 and 26.
a + b = 87
a - b = 37
Add the two equations.
2a = 124
You should be able to take it from here.