The sum of two numbers is 22. Three times one number increased by five is 35 What are the equations you would use
Let's call the two numbers x and y. From the given information, we can set up two equations as follows:
Equation 1: x + y = 22
This equation represents the sum of the two numbers being equal to 22.
Equation 2: 3x + 5 = 35
This equation represents three times one number increased by five being equal to 35.
To solve this problem, we can use the following equations:
Equation 1: x + y = 22
(This equation represents the sum of two numbers being equal to 22, where x and y are the two numbers)
Equation 2: 3x + 5 = 35
(This equation represents three times one number increased by five being equal to 35, where x is the number)
These two equations will help us find the values of x and y that satisfy both conditions mentioned in the problem.
To solve this problem, we can use a system of equations. Let's assign variables to the numbers mentioned in the question.
Let's say the two numbers are x and y.
The first equation states that the sum of two numbers is 22:
x + y = 22
The second equation states that three times one number increased by five is 35:
3x + 5 = 35
Now we have the two equations:
1) x + y = 22
2) 3x + 5 = 35
To find the solution to this system of equations, we can use various methods, such as substitution or elimination. Let's use the substitution method:
From equation 1, we can solve for x:
x = 22 - y
Substitute the value of x from equation 1 into equation 2:
3(22 - y) + 5 = 35
Simplify equation 2:
66 - 3y + 5 = 35
Combine like terms:
-3y + 71 = 35
Rearrange the equation:
-3y = 35 - 71
Simplify the right side:
-3y = -36
Divide both sides by -3:
y = (-36) / (-3)
y = 12
Now substitute the value of y back into equation 1 to solve for x:
x + 12 = 22
Subtract 12 from both sides:
x = 22 - 12
x = 10
So, the two numbers are x = 10 and y = 12.