help with math. i'm desperate?

Question

The greater of two consectutive even integers is 20 more than twice the smaller. Find the integers.

The difference of two integers is 9. Five times the smaller is 7 more than 3 times the larger. Find the numbers.

A 2000 L tank containing 550 L of water is being filled with water at the rate of 75 L per minute from a full 1600 tank. How long will it be before the two tanks have the smae amount of water?

A boat weighs 1500 lb more than its motor and 1900 lob more than its trailer. Together the boat and motor wegih five times as much as the trailer. HOw much does the boat weigh.

dude i do NOT get these problems. can someone solve them and explaim or show work is possible. MUCH APPRECIATED!!!!

Answer 1

I'm not absolutley positive, but I think the fourth one may use system of equations but with three equations. Solve for a variable on one, plug in to the other two, subsitute for all the variables and I guess add to find your answer. Or you could use elimination. Eliminate using two of the equations in the system of your choice, then use another two (you can use one over, obviously), and from there I think it's okay to substitute using one of the found variables, but I cant be sure. I havent actually learned this yet.

Answer 2

#2 is a system of equations

Difference of 2 integers is 9 means x - y = 9

Five times the smaller is 7 more than 3 times the larger. Since x - y is a positive number, y must be smaller than x. So the equation is: 5y = 7 + 3x

Leave the first equation as is:
x - y = 9

Rewrite the second one by subtracting 3x from both sides and 5y from both sides. You end up with:
-3x + 5y = 7

Written together:

x - y = 9
-3x + 5y = 7

Multiply the top equation by 3: 3(x - y = 9). You do this so that you can reduce the two equations w/ two unknowns to one equation with one unknown that you can solve for.

Then you'll have:
3x - 3y = 27
-3x + 5y = 7

Add the sets of equations together:
3x - 3y = 27
-3x + 5y = 7
-------------------
3x + (-3x) = 0 (any number plus it's negative is zero)

(-3y) + (5y) = 2y (it's just 5y - 3y backwards)

27 + 7 = 34

And then you have one equation with only one unknown that you can solve:
2y = 34 which means y = 17.

Plug 17 into either of the original equations. It's easiest to use the first one

x - y = 9
x - 17 = 9

Add 17 to both sides to solve for x:
x = (9 + 17) = 26

You can check it by plugging the numbers into the second equation.

Answer: x = 26, y = 17

I hope that helped.

Answer 3

1) x = 1st integer
x + 2 = 2nd integer

(x+2) - 20 = 2x

x = -18

So -18 and -16




2)

x - y = 9
5x = 3y+7

Now, multiply the first equation by -5 to eliminate the x's.

-5x + 5y = 9
5x -3y = 7

Add together

2y = 16

y = 8
x = 17


3)

550 + 75 x = 1600 - 75 x
150 x = 1050
x = 7 minutes

4) Boat (B), Motor (M), Trailer (T),

B = 1500 + M
B = 1900 + T

You can set the rest up....

Answer 4

First one: two consecutive even integers, so that's something like 4 and 6 or 20 and 22. Let's call them n and n+2. Twice the smaller is 2n. Twenty more than twice the smaller is 2n + 20.
So n+2 = 2n + 20. Subtract 2 from both sides to get
n = 2n +18, Subtract 2n from both sides to get
-n = 18 therefore n = -18. So n + 2 = -16.
The second problem uses very similar reasoning.

Answer 5

Problem #1. . . .

First integer = x

Second integer = x +2

x + 2 = 20 + 2x

x - 2x = 20 - 2

-x = 18

x = -18

x + 2 = -16

Checking: -16 =? 2(-18) +20

-16 =? -36 + 20

-16 = -16. My faith in math is restored. (Whew.)

Setting up #2 but not doing it--

x-y=9. -y=9-x. y=x-9.

Substitute: x=First integer; x-9=Second integer.

5 (x-9) = 7+ 3x.

Go for it.

Answer 6

here is the first equation

1) let a = 1st even consecutive integer
let a+2= 2nd even consecutive integer

a+1= 2(a)+20