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.

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 (2×8.8).

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

* Gustavo should check your answer again.

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.

width=12