The sum of two numbers is 22. Three times one number increased by five is 35.
a) What are the equations you would use?
x+y=22 and 3x+5=35
b) What are the two numbers? Response area and
The two numbers are x and y, where x+y=22.
To find the two numbers, we can solve the system of equations:
x + y = 22 ---(1)
3x + 5 = 35 ---(2)
We can solve equation (1) for x by subtracting y from both sides:
x = 22 - y
Substituting this value of x into equation (2):
3(22 - y) + 5 = 35
66 - 3y + 5 = 35
71 - 3y = 35
-3y = 35 - 71
-3y = -36
y = -36/-3
y = 12
Now, substitute the value of y into equation (1) to solve for x:
x + 12 = 22
x = 22 - 12
x = 10
Therefore, the two numbers are 10 and 12.
To solve this problem, we can set up a system of equations. Let's assign variables to the two numbers.
Let's say the first number is x and the second number is y.
According to the problem, the sum of the two numbers is 22, so we can write the equation:
x + y = 22 (Equation 1)
The problem also states that three times one number increased by five is 35. So, we can write another equation:
3x + 5 = 35 (Equation 2)
To find the values of x and y, we need to solve this system of equations.
Now, let's solve Equation 1 for y:
y = 22 - x
Substitute this expression for y into Equation 2:
3x + 5 = 35
Simplify the equation:
3x = 30
Divide both sides by 3:
x = 10
Now, substitute the value of x back into Equation 1:
10 + y = 22
Subtract 10 from both sides:
y = 12
Therefore, the two numbers are x = 10 and y = 12.