middle school math. Help?!

Question

Separate 84 into two parts so that one part is 9 less than twice as much as the other. Find each part.

Answer 1

Separating 84 seems to mean that we need to determine what 2 numbers can add up to 84.

84 = x+y

Then we need to figure out the two numbers or "parts" which are the variables x and y. The variables are usually lower case letters of some sort but they are really just placeholders for numbers.

If we say that one part is x then we can follow : x is 9 less (x= - 9) than twice the other : 2y because y is the other. combined, the words give us:

x = 2y - 9

We can plug in x into the previous (84 = x + y) so we only need to solve for one variable:

84 = (2y-9) + y

We need to do algebra to find y by adding 9 to both sides of the equation which gives:

93 = 2y + y

Then 93 = 3y : divide 3 on both sides : 31 = y

If we fill in y = 31 into the 84 = x + y ----------> 84 = x + 31, then x = 53

Checking the answer : one part is 31, then the second part is 9 less than twice the other part: 2(31)-9 which is 62 - 9 = 53

Answer 2

x + y = 84

y = 2x - 9

Substitute:

x + 2x - 9 = 84

3x = 93

x = 31

y = 53