I need to know how to do these math problems.?

Question

Pleas show work/explain how you got the answer.

The sum of two numbers is two. The difference between eight and twice the smaller number is two less than the larger. find the two numbers.

A real estate agent sold two homes and recieved commissions totaling $6000. The agent's commission on one home was one and one-half times the comission on the second home. Find the agents comission on each home.

A university employs a total of 600 teaching assistants abd research assistants. There are three times as many teaching assistants than research, Fund the number if research assistants employed by the university.

a 20-foot board is cut into two pices. Twice the length if the shorter piece is 4 ft more than the length of the longer piece. Find the length of the shorter piece.

A wire 12 ft long is cut inot two pieces. Each piece is bent into the shape of a squaer. The perimeter of the large square is twice the perimeter of the smaller square.Find the perimeter of the larger squa

Answer 1

You need to read each part of the word problem and set it up as an algebra problem. Let x be the thing you are looking for, then write your word problem in terms of x.

Here, I will do one for you, but you should look at my example then try the others yourself. You will learn more that way. If by chance some suckers come along and give you all the answers and you just copy them down from here to your homework, then you are only cheating yourself. And I will be ordering my fries and burger from you in a couple of years when you are out of high school! :)

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PROBLEM:

The sum of two numbers is two. The difference between eight and twice the smaller number is two less than the larger. find the two numbers.

SOLUTION:

Let x and y be the two numbers.

"The sum of two numbers is two" --> this means x+y = 2
Since we want to only deal with one variable, we could also write y as 2-x.

"The difference between eight and twice the smaller number is two less than the larger."

Either x or y could be the smaller number. It doesn't matter, since we are using arbitrary variables. So we'll say x is the smaller number, OK. That means y, or 2-x, is the larger number.

So translating the above sentence, we get "The difference between eight and twice the smaller number is two less than the larger" means 8-2x = (2-x) - 2

.. "twice the smaller number" means 2x
.. "the difference between 8 and twice the smaller number" means 8-2x
.. "is 2 less than the larger" means y-2, or (2-x) - 2

So, now you have a complete (and very easy) algebraic problem you can solve:

8-2x = (2-x) - 2

Get your x's on one side of the equation to solve for x:

8 - 2x = 2 - x - 2

8 = x

since y = 2-x, you can now solve for y = -6

HTH! :-)

Answer 2

A real estate agent sold two homes and recieved commissions totaling $6000. The agent's commission on one home was one and one-half times the comission on the second home. Find the agents comission on each home.

Define all terms
X+Y = 6000
show relationship between comissions
X = 1.5Y
substitute Y for X
1.5Y +Y =6000
simple addition will get you the next step
then divide for the answer

Answer 3

All these questions are of the form "two equations, two unknowns". The questions give you the clues to create two equations that involve two unknown quantities, call them x and y.

Take the last one. If the wire is 12 ft, you know the lenght of the two pieces (there are your two unknowns). So x + y = 12. The other clue is the perimeter of one square is twice the perimeter of the other. So x = 2y. Once you have the equations set up, use one equation to isolate the value of one variable, and substitue it into the other equation. x = 2y already isolates x in terms of y, so in the equation x + y = 12 substitute 2y for x. Now you get 2y + y = 12. Solve for y, then solve for x.

Answer 4

-7= 3x-8 when putting -8 to the other side of equation, the sign will change, so it's -7+8= 3x which means 1=3x therefore x= 1/3 and don't worry about the order, it doesn't matter! there's a rule in math about the order! you can easily check it by substituting 1/3 into the equation i.e -7= 3*1/3-8 -7=-7!!!

Answer 5

I worked this problem about 10 times and got the same result as your first respondent. I also let x be the smaller number and when i solved the problem it turned out to be 8, the larger number, just as your first respondent did. Curious to see if your math book has an error.

Answer 6

q1. x + y = 2
8 - 2x = y - 2

q2. x + y = 6000
3/2x = y

q3. x + y = 600
3x = y

q4. x+y = 20
2x + 4 = y

q5. x+y = 12
2x = y

Answer 7

it could be -2 and 4
i don't know the rest