The mean of two unknowns TECH MATH HELP!!

Question

The mean of two numbers is 28. Find the numbers if 3 times one of the numbers equals half the other number. Hint. The mean of x and y is (x+y)/2 = 1/2(x+y)

I honestly don't understand what I'm supposed to do here can someone help me out? Thank you!

Answer 1

(x+y)/2 = 28

so x + y = 28 x 2 = 56

3x = 1/2 y.

Multiply through by 2.

6x = y.

x+y = 56

y = 6x

x + 6x = 56

7x = 56

x = 8

y = 6 x 8 = 48.

Answer 2

Hi Sabreena! We need to keep in mind our goal: find the two numbers that fit these requirements.

Step 1: State what you know

We are given the information that the mean, (x+y)/2, equals 28. That gives us:

(x+y)/2 = 28.

We also know the relationship of the two numbers. Three times one number equals half of the other number. That can be expressed like this:

3x = 1/2y

Step 2: Get a variable alone

We are going to use that second equation and get one variable alone. Let's choose to get y by itself. To do this, we multiply each side by 2. That gives us:

6x = y OR y = 6x.

Step 3: Plug in y in terms of x

Now we will plug y = 6x into our original equation, (x+y)/2 = 28. That gives usL

(x + 6x)/2 = 28.

Step 4: Solve for x

Solve for x!

(7x)/2 = 28

7x = 56

x = 8.

Great job! We got our first number! We know one of the numbers is 8.

Step 5: Solve for y

Now that we know what x is, we can plug it into (x+y)/2 = 28.

(8 + y)/2 = 28

(8 + y) = 56

y = 48

Awesome! Now we have the second number! You have finished the problem!

If anything is unclear, please let me know! I would be happy to clear up any confusion.