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The sum of two numbers is 22. Three times one number increased by five is 35. (4 points) a) What are the equations you would use? ¦ and ¦ b) What are the two numbers? and
a) The equations we would use are:
Equation 1: x + y = 22 (sum of two numbers is 22)
Equation 2: 3x + 5 = 35 (three times one number increased by five is 35)
b) To solve the equations, we can use substitution or elimination method.
Using the substitution method:
From Equation 1, we can rearrange it to express x in terms of y:
x = 22 - y
Substituting this value of x into Equation 2:
3(22 - y) + 5 = 35
66 - 3y + 5 = 35
-3y + 71 = 35
-3y = 35 - 71
-3y = -36
y = -36 / -3
y = 12
Substituting this value of y back into Equation 1:
x + 12 = 22
x = 22 - 12
x = 10
So, the two numbers are x = 10 and y = 12.
a) The equations we would use are:
1) x + y = 22
2) 3x + 5 = 35
b) To find the value of x and y, we will solve these equations simultaneously.
Let's solve equation 1 for y:
x + y = 22
y = 22 - x
Now substitute this expression for y in equation 2:
3x + 5 = 35
3x = 35 - 5
3x = 30
x = 10
Now substitute the value of x in equation 1 to find y:
10 + y = 22
y = 22 - 10
y = 12
Therefore, the two numbers are x = 10 and y = 12.
To solve this problem, we can set up a system of equations with two variables. Let's call the unknown numbers x and y.
Based on the given information, we can write two equations:
Equation 1: x + y = 22
The sum of the two numbers is 22.
Equation 2: 3x + 5 = 35
Three times one number (x) increased by five equals 35.
To find the values of x and y, we can solve this system of equations.
a) To solve this system of equations, we can use the method of substitution or elimination. Let's choose the substitution method.
First, let's isolate one variable in one equation and substitute it into the other equation. From Equation 1, we can isolate y:
y = 22 - x
Now, substitute this value of y into Equation 2:
3x + 5 = 35
3x = 35 - 5
3x = 30
x = 30/3
x = 10
Substitute the value of x back into Equation 1 to find y:
10 + y = 22
y = 22 - 10
y = 12
b) The two numbers are 10 and 12.