The sum of two numbers is 22. Three times one number increased by five is 35.
a) What are the equations you would use? Response area and Response area
b) What are the two numbers? Response area and Response area
a) The equations would be:
x + y = 22 (Equation 1)
3x + 5 = 35 (Equation 2)
b) Solving the equations:
From Equation 1, we can subtract x from both sides to isolate y:
y = 22 - x (Equation 3)
Substituting Equation 3 into Equation 2, we get:
3x + 5 = 35
Subtracting 5 from both sides:
3x = 30
Dividing both sides by 3:
x = 10
Plugging x = 10 into Equation 1, we can find y:
10 + y = 22
Subtracting 10 from both sides:
y = 12
So, the two numbers are 10 and 12.
a) The equations that can be used to solve the problem are:
1. Equation 1: x + y = 22 (where x and y are the two numbers)
2. Equation 2: 3x + 5 = 35 (where x represents one of the numbers)
b) To find the two numbers, we need to solve these equations simultaneously.
From Equation 1, rearrange it to solve for x:
x = 22 - y
Substitute this value of x into Equation 2:
3(22 - y) + 5 = 35
Simplify the equation:
66 - 3y + 5 = 35
Combine like terms:
-3y + 71 = 35
Subtract 71 from both sides:
-3y = 35 - 71
-3y = -36
Divide both sides by -3:
y = (-36) / (-3)
y = 12
Substitute the value of y back into Equation 1 to find x:
x + 12 = 22
x = 22 - 12
x = 10
Therefore, the two numbers are x = 10 and y = 12.
a) The information given can be translated into two equations:
1) The sum of two numbers is 22:
x + y = 22
2) Three times one number increased by five is 35:
3x + 5 = 35
b) To find the two numbers, we need to solve the system of equations formed by these two equations. Here's how you can do it:
Step 1: Simplify the second equation:
3x + 5 = 35
Subtract 5 from both sides:
3x = 30
Step 2: Solve for x:
Divide both sides by 3:
x = 10
Step 3: Substitute the value of x into the first equation to find y:
10 + y = 22
Subtract 10 from both sides:
y = 12
Therefore, the two numbers are 10 and 12.