The sum of two numbers is 38.when 8 is added to twice one of the numbers,the result is 5 times the other number.Find the two numbers
Let the number be a and 38-a
To solve this problem, let's break it down into steps:
Step 1: Set up the equations
Let's assume the first number is 'x' and the second number is 'y'. We are given two pieces of information:
1) The sum of the two numbers is 38, so we can write the equation: x + y = 38
2) When 8 is added to twice one of the numbers, the result is 5 times the other number. This can be written as: 2x + 8 = 5y
Step 2: Solve the equations
To solve this system of equations, we can use substitution or elimination method. Since the first equation is already in terms of 'x', let's solve for 'x' in terms of 'y' and substitute it in the second equation.
From the first equation, we can isolate 'x':
x + y = 38
x = 38 - y
Now substitute this value of 'x' into the second equation:
2(38 - y) + 8 = 5y
Simplify the equation:
76 - 2y + 8 = 5y
84 - 2y = 5y
Combine like terms:
84 = 7y
y = 12
Step 3: Find the value of 'x'
Plug the value of 'y' back into one of the original equations:
x + y = 38
x + 12 = 38
x = 38 - 12
x = 26
Therefore, the two numbers are 26 and 12.