The sum of the two numbers is 71. One of the numbers is 24 less than four times the other number. What are the two numbers I am thinking of?
n + 4n - 24 = 71
5n = 95
n = ?
n=19
Let's solve this step-by-step.
Let's assume the first number is 'x' and the second number is 'y'.
According to the given information, we have two equations:
Equation 1: x + y = 71 (the sum of the two numbers is 71)
Equation 2: x = 4y - 24 (one number is 24 less than four times the other number)
We can solve this system of equations using substitution or elimination method.
Let's use substitution method:
Substitute x in Equation 1 with the expression from Equation 2:
4y - 24 + y = 71
Combine like terms:
5y - 24 = 71
Add 24 to both sides of the equation:
5y = 95
Divide both sides by 5:
y = 19
Now, substitute y = 19 back into Equation 1:
x + 19 = 71
Subtract 19 from both sides:
x = 52
So, the two numbers you are thinking of are 52 and 19.
To solve this problem, let's assign variables to the unknown numbers. Let's call one number "x" and the other number "y".
From the given information, we have two pieces of information:
1. The sum of the two numbers is 71: x + y = 71
2. One of the numbers (let's say "x") is 24 less than four times the other number "y": x = 4y - 24
Now we can solve the system of equations to find the values of x and y.
First, we can substitute the value of x from equation 2 into equation 1:
4y - 24 + y = 71
Combining like terms:
5y - 24 = 71
Next, we can isolate the variable y by adding 24 to both sides:
5y = 95
Finally, divide both sides of the equation by 5 to solve for y:
y = 19
Now, substitute the value of y back into equation 1 to find x:
x + 19 = 71
Subtracting 19 from both sides:
x = 52
Therefore, the two numbers you are thinking of are 19 and 52.