Question: separate 84 into two parts so that one part is 9 less than twice as much as the other. find each part.

53+31=84

Step-by-step explanation:

Equations, equations, equations, kemosabe. Remember to make your equations.

1. What do we know? We know that two numbers added together equal 84.

This can be represented as x+y=84

But now we've been given some extra intel that one of the numbers (for simplicity's sake, let's say it's x) is 9 less than TWICE the other number (y).

2. Update your equation.

The equation for x currently looks like: X=2y-9

Your original equation is: x+y=84.

Sub in the x value we JUST determined for x in the OG equation.

2y-9+y=84

3. Combine Like terms (variables) on one side.

2y-9+y=84.

You want to try and isolate variable with the coefficient, so you first can combine 2y+y to get 3y.

3y-9=84

4. Isolate the variable.

3y-9=84.

3y-9+9=84+9

3y=93

3y/3 = 93/3

y=31.

5. Re-access.

Goodie, you've found the Y value!

. . .now what? USE IT!!

You now take your original equation, x+y=84, and sub in the value you JUST determined for y.

x+31=84

6. Isolate (again).

x+31=84

x+31-31=84-31

x=53

7. Re-access (again)

Goodie, you've found the X value!

Now what?

Well, now we know that, in our equation, x=53 and y=31.

This means 53+31=84.

8. CHECK VIA THE RESTRAINTS!

One number must be exactly 9 less than TWICE as much of the other number.

Obviously, the number that should be twice as much will always be the biggest number, so, in this case, it's 53.

How can we determine if 53 is 9 less than twice as much as 31?

Easy. First, find out how much twice as much of 31 is. 31*2=62.

Subtract 9, and we should get our x variable as the answer.

62-9=. . .53!!!

8. Wrap up.

Your OG equation is x+y=84.

Now, your equation will be: 53+31=84.

31 and 53

Step-by-step explanation:

let the two parts be a and b, then the following equation describes the problem:

1) 84 = a + b

the condition on a and b is:

2) a = 2b - 9

Combining equations 1 and 2:

84 = (2b - 9) + b

84 = 3b - 9

93 = 3b

b = 31

a = 84 - b

a = 53