The sum of two numbers is 22. Three times one number increased by five is 35.
(a) What are the equations you would use? ________ and ________
(b) What are the two numbers? ________ and ________
wrong again. Clearly, 13 and 9 do not satisfy the second equation.
3x+5 = 35
x = 10
so y = 12
I apologize for the mistake. You are correct.
The correct equations are:
1. x + y = 22
2. 3x + 5 = 35
Using the second equation: 3x + 5 = 35, we can solve for x:
3x = 30
x = 10
Substituting x = 10 back into the first equation: 10 + y = 22
y = 12
Therefore, the two numbers are 10 and 12.
(a) The equations we would use are:
1. x + y = 22 (since the sum of two numbers is 22)
2. 3x + 5 = 35 (since three times one number increased by five is 35)
(b) To solve for the two numbers, we can use the equations as follows:
From equation 1, we can rearrange it to solve for one variable:
x = 22 - y
Substitute the x value in equation 2:
3(22 - y) + 5 = 35
Simplify and solve for y:
66 - 3y + 5 = 35
-3y = 35 - 66 - 5
-3y = -36
y = (-36)/(-3)
y = 12
Substitute the y value back into equation 1 to find x:
x + 12 = 22
x = 22 - 12
x = 10
Therefore, the two numbers are 10 and 12.
(a) To solve this problem, we can set up two equations. Let's use variables to represent the two numbers. Let's call the first number 'x' and the second number 'y'.
The first equation is based on the given statement "The sum of two numbers is 22." This can be written as:
x + y = 22
The second equation is based on the statement "Three times one number increased by five is 35." This can be written as:
3x + 5 = 35
(b) Now, let's solve these equations to find the values of 'x' and 'y'.
From the first equation, we can solve for 'x' in terms of 'y' by subtracting 'y' from both sides:
x = 22 - y
Now we substitute this expression for 'x' into the second equation:
3(22 - y) + 5 = 35
Expanding and simplifying:
66 - 3y + 5 = 35
-3y + 71 = 35
Next, we isolate 'y' by subtracting 71 from both sides:
-3y = 35 - 71
-3y = -36
Finally, we solve for 'y' by dividing both sides by -3:
y = -36 / -3
y = 12
Now that we have the value of 'y', we can substitute it back into the first equation to find 'x':
x + 12 = 22
x = 22 - 12
x = 10
So, the two numbers are 10 and 12.
(a) The equations we would use are:
1. x + y = 22 (where x and y are the two numbers)
2. 3x + 5 = 35
(b) The two numbers are 13 and 9.