Need serious help correcting incorrect math test problems?

Question

I got a math test back, and did poorly. But if we correct our mistakes we get 1/2 credit on what we missed. Problem is, I don't know how to solve them correctly. Please help!

Solve Using the Elimination method:
4y - 3x = 4
6x + 5y = 33/4



The perimeter of a rectangle is 88. the length of the rectangle is two more than twice the width. Find the dimensions of the rectangle.



Dick Fields has chashews that sell for $7 a pound and peanuts that sell for $5.50 a pound. How much of each must he mix to get 20 pounds of a mixture that sells for $6.00 per pound?


Elimination
.3x = .2y + .4
-1.2x + .8y = -1.6


Elimination again
3/2a + b = 6
a - 5/2b = -4



I know it's a bit much, but I'm working on them here as I await any help I can get. Thanks so much!

Answer 1

All right, I'll help you with one - the cashew problem:

Set up the variables:

Cashews = x
Peanuts = y

First, you'd take 20lbs. x $6 = $120

These are your two equations:
x + y = 20
7x + 5.5y = 120

Then, get either x or y by itself in the first equation, I'll do x:

x + y (-y) = 20 (-y)

x = 20 - y

Now that you have x by itself, plug in 20 - y in for x:

7(20 - y) + 5.5y = 120

Distribute:

140 - 7y + 5.5y = 120

Combine like-terms:

140 - 1.5y = 120

Subtract 140 from both sides:

140 (-140) -1.5y = 120 (-140)

-1.5y = -20

Divide both sides by -1.5

-1.5y (/-1.5) = -20 (/-1.5)

y = 13 1/3

So, there's 13 1/3 lbs of cashews which means there's 6 2/3 lbs of peanuts. If you figure it all out for y, you'll get the same thing. Hope this helps and the steps make sense. Basically, all the other problems are the same way in figuring it out, just different numbers.

Answer 2

okay, i'll try and help you with 2 or maybe 3.

1. 4y - 3x = 4
6x + 5y = 33/4

* 20y - 15x = 20 [multiplying 5 on both sides]
24x + 20y = 33 [multiplying 4 on both sides]
--------------------------
-39x = -13 [subtracting 2nd equation from 1st]
therefore:
x = 1/3 [ dividing by 39 on both sides]

so, if x=1/3 then:
4y -3x = 4
substitute 1/3 for x in the equation
4y - 3 x 1/3 = 4
4y = 5
therefore
y= 5/4

Answers: [x = 1/3 and y = 5/4]

2. Your rectangle question:)
* Width = w
* Length = 2(2w) = 4w
Therefore:
Perimeter = 2length + 2width
88 = 2(4w) + 2w
88 = 8w + 2w
88 = 10w
therfore the width = 8.8
so the length is 4w therefore:
l = 4w
= 4 x 8.8
= 35.2
the width is 8.8 and the length is 35.2 [i.e 2 more than twice the width --> 2 x (2x8.8).

*if you substitute the values above into the formula for the perimeter you'll get exactly 88.

* Gustavo should check your answer again.

Answer 3

If you ask separate questions, we get more points.

4y - 3x = 4
6x + 5y = 33/4
Multiply #1 by 2
8y - 6x = 8
Add to #2 to eliminate 6x:
8y + 5y = 4 + 33/4
Gather like terms:
13y = (16 + 33)/4
Multiply both sides by 4:
52y = 49
You may have copied this wrongly.

Answer 4

So the question is rather this: 4 * sqrt12 * 3 * sqrt6 in case you situations the 4 and 3 you get 12, so it is comparable to = 12 * sqrt12 * sqrt 6 Now, sqrt12 = sqrt(6*2) = sqrt6 * sqrt2 so... = 12 * sqrt6 * sqrt6 * sqrt2 = 12 * 6 * sqrt2 = 72sqrt2

Answer 5

the rectangle is length= 28
width=12