The sum of two numbers is 22. Three times one number increased by five is 35.
What are the two numbers?
___ and ___
Let's say the two numbers are \(x\) and \(y\).
From the information given, we can form the following equations:
1) \(x + y = 22\) (The sum of two numbers is 22)
2) \(3x + 5 = 35\) (Three times one number increased by five is 35)
To solve these equations, we can start by rearranging equation 2) to solve for \(x\):
\[3x + 5 = 35\]
Subtract 5 from both sides:
\[3x = 30\]
Divide both sides by 3:
\[x = 10\]
Now that we know \(x = 10\), we can substitute this value into equation 1) to find \(y\):
\[10 + y = 22\]
Subtract 10 from both sides:
\[y = 12\]
Therefore, the two numbers are 10 and 12.
Let's solve this step-by-step.
1. We are given that the sum of two numbers is 22. Let's call the numbers x and y.
So, the first equation is: x + y = 22.
2. We are also given that three times one number increased by five is 35.
So, the second equation is: 3x + 5 = 35.
To solve these equations simultaneously, we can use the substitution method. Let's solve the second equation for x:
3x + 5 = 35
Subtract 5 from both sides:
3x = 30
Divide both sides by 3:
x = 10
Now, substitute the value of x into the first equation:
10 + y = 22
Subtract 10 from both sides:
y = 22 - 10
y = 12
Therefore, the two numbers are 10 and 12.
To find the two numbers, we can solve this problem using a system of equations. Let's denote the two numbers as x and y.
From the first statement, "The sum of two numbers is 22," we can write the equation:
x + y = 22 ----(Equation 1)
From the second statement, "Three times one number increased by five is 35," we can write the equation:
3x + 5 = 35 ----(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve using the substitution method:
1. Solve Equation 1 for x:
x = 22 - y
2. Substitute the value of x in Equation 2:
3(22 - y) + 5 = 35
Simplifying the equation,
66 - 3y + 5 = 35
71 - 3y = 35
3. Move the constants to one side:
-3y = 35 - 71
-3y = -36
4. Solve for y:
y = (-36)/(-3)
y = 12
5. Substitute the value of y back into Equation 1:
x + 12 = 22
x = 22 - 12
x = 10
Therefore, the two numbers are x = 10 and y = 12.