help me..?

Question

-Jim's weekly pay is two thirds of Alicia's. Together they earn $800 per week. What is each person's weekly pay?

-If one side of a square is increased by 8 cm and an adjacent side is decreased by 2 cm, a rectangle is formed whose perimeter is 40 cm. Find the length of a side of the square.

-The sum of the measures of the angles of a pentagon is 540 degrees. The degree of measures of the angles of a pentagon are consecutive even integers. Find the measure of the largest angle.

Answer 1

Jim's pay (J) is (=) two thirds of Alicia's (2/3)A

J=(2/3)A

Together (J+A) they earn $800 (=800)

J+A=800

(2/3)A+A=800

(2/3)A+(3/3)A=(5/3)A=800

(3/5)(5/3)A=800*(3/5)

A=480
J+480=800
J=800-480=320
Alicia makes $480 and Jim makes $320

(Double check by plugging in)
J=(2/3)A
Does 320=(2/3)480? Yes
J+A=800
Does 320+480+800? Yes

So the answer was correct: Alicia makes $480 and Jim makes $320

If one side of a square is increased by 8cm and an adjacent side is decreased by 2cm, a rectangle is formed whose perimeter is 40cm.

By definition a square has 4 sides that are equal in length. If we add 8 cm to one side and 2 cm to the other we would have 2 sides of the rectangle equal to (x+8) and two more equal to (x+2). The perimiter is 2L+2W so 2(X+8)+2(X+2)=40
2X+16+2X+4=40
4x=20
X=5
That would be the length of the square

Sorry I have to go and can't help on the last one right now....Time for lunch

Answer 2

I hope you do algebra.

Jim's pay is 2/3s that of Alicia. Call Alicia X, then Jim would be (2/3)X.

X+(2/3)X=800. Now, do the math. You get (5/3)X=800.
(This is because X is the same as (3/3)X, or (5/5)X, or whatever, since you are multiplying by 1).

Take 800, and divide it by 5/3. You should get $480. This is the value of X, which is Alicia's pay. Jim get's 2/3s of this, so figure out what that would be (either by subtracting $480 from $800 to see what he would make, or by figuring out what a third of $480 then multiplying it by 2.) I'm not going to tell you what Jim makes - you're smart enough to figure it out.
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Perimeter Question
Since you start with a square, all four sides have to be the same size. We'll call the length of the top and bottom sides "X", and the length of the two sides "Y".

Since there are four sides, your original perimeter is represented by:
X+Y+X+Y=original perimeter, that doesn't matter right now.

Since you are increasing one side by 8cm, and decreasing the other by 2cm, and ending up with a perimeter of 40cm, you end up with the following:
(X+8)+(Y-2)+(X+8)+(Y-2)=40 cm (you end up with a rectangle, so opposite sides have to be the same length, so you are really changing the lengths of all four sides.
You can then remove your brackets and do the math.
X+8+Y-2+X+8+Y-2=40 cm
X+X+Y+Y+8-2+8-2=40 cm
2(X)+2(Y)+12=40 cm
Then you subtract 12 from both sides of your equation to find:
2(X)+2(Y)=28 cm.

Since the square had sides of the same length before, X and Y must equal one another, so you know that the length of any one side must be 28cm divided by 4. I'll let you figure this out as well.

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Pentagon question:
You've got a pentagon (5 sides) and 540 degrees of angles. How many angles are there in a pentagon? Five, of course.
You can do this by trial and error, which would be faster, after doing a little math, or you could do it the long way. I'll demonstrate both methods.
Take 540 degrees, then divide this by 5 to figure out the average angle. You end up with 108 degrees. Since you have five angles, and they are all consecutive even integers, you may wish to pick two even numbers above, and two below, then add them together to see if it's right (108+2 is 110, 108+4 is 112, 108-2 is 106, and 108-4 is 104. Add these up: 108+110+112+106+104=540. That works out.
The longer and likely the way you should learn to do it, is to give each angle a variable. Let's use A, B, C, D, and E.
A+B+C+D+E=540.
Since you know that these five are consecutive even integers, you know that:
B=A+2
C=A+4
D=A+6
E=A+8
Knowing this, you can subsititute into the original equation:
A+(A+2)+(A+4)+(A+6)+(A+8)=540
Then, you can solve by removing the brackets:
A+A+A+A+A+2+4+6+8=540
5(A)+20=540.
Now subtract 20 from each side:
5A=520
Now divide both sides by 5 to get A.
A=104.
Now substitue A back into the equations for the four other sides to find each length. Add all these up at the end to check that they add to 540, and you should be correct.

Hope this helps.

Answer 3

Jim's weekly pay is two thirds of Alicia's. Together they earn $800 per week. What is each person's weekly pay?
Let x= Alicia' pay, the Jims pay is 2/3x
So x+2x/3 = 800
3x+2x = 2400
5x= 2400
x= 480 = Alicia's pay
2x/3 = 320 = Jim's pay

-If one side of a square is increased by 8 cm and an adjacent side is decreased by 2 cm, a rectangle is formed whose perimeter is 40 cm. Find the length of a side of the square.
Let x = side of square
Then x+8 = length of rectangle and
x-2 = width of rectangle
Pereimeter = 2(length + width)=2(x+8+x-2) = 4x +12
4x+12=40
4x = 28
x = 74 = side of original square.

The sum of the measures of the angles of a pentagon is 540 degrees. The degree of measures of the angles of a pentagon are consecutive even integers. Find the measure of the largest angle.

Pentagon has 5 interior angles. If they are consecutive even numbers, they are 2x, 2x+2, 2x+4, 2x+6 , and 2x+8
There sum is 10x + 20 = 540
10x = 52x= 52
Largest = 2x +8 = 2(52) + 8 = 112 degrees.

Answer 4

For word problems, what we always want to do is assign our variable x to the thing/concept being most compared to.

1) Notice that it says Jim's weekly pay is two-thirds of Alicia's. Since Alicia's pay is the thing being compared to,
Let x = Alicia's pay. That means
Jim's pay is equal to (2/3)x.

Together, they earn 800 per week, so

x + (2/3)x = 800

We solve for x as per the usual methods. Let's multiply both sides by 3.

3x + 2x = 2400
5x = 2400
x = 480

Therefore, Alicia's weekly pay is $480. To get Jim's weekly pay, earlier we said it was (2/3)x. This time, we *have* the value for x, so Jim's pay is (2/3)(480) = 960/3 = 320.
So Jim's pay is $320, Alicia's pay is $480.

2) Let x be the side of the square.
Increasing a side of a square by 8 cm would make the side
(x + 8), and decreasing the adjacent side by 2 cm would make that adjacent side equal to (x - 2). We're given that the perimeter of this rectangle is 40 cm.

The formula for the area of the rectangle would be

P = (size of length) + (size of width) + (size of length) + (size of width)

4 sides to a rectangle, 4 things to add up. Subsequently, this means we have two of each side.

P = 2(size of length) + 2(size of width)

Note that we have the length; it's x + 8. We also have the width; it's x - 2. Therefore

P = 2(x + 8) + 2(x - 2)

We know the value of P though; it's 40, so

40 = 2(x + 8) + 2(x - 2)

Now we solve as per usual algebraic methods.

40 = 2x + 16 + 2x - 4
40 = 4x + 12
28 = 4x, therefore
x = 7

So the side of the square is 7.

Answer 5

(1) J = 2A/3
J + A = 800
2A/3 + 3A/3 = 800
5A/3 = 800
5A = 2400
A = 480
J = 320.

(2) Side of square = x
Semi-perimeter of rectangle = 40cm/2 = 20cm
20cm = x+8 + x-2
= 2x+6
2x = 14
x = 7.

(3)You need consecutive even integers that add to 540.
Setting the middle one as X, the angles then are:
x-4
x-2
x
x+2
x+4

(x-4) + (x-2) + x + (x+2) + (x+4) = 540
5x = 540
x = 108

So the angles are 104, 106, 108, 110 and 112; the largest of which is 112 degrees.

Answer 6

- make jims share 2 parts and alicias share 3 parts, so they have the ratio correct, then add them together.. so 5 parts is 800

2x + 3 x = 800 -> 5x = 800 -> x = 160

so jim is 2 x 160 = 320 and alicia is 3 x 160 = 480 and 320 + 480 = 800



originsal square is 7x7, new rectangle is 15x5 with P=40


need to add 5 consecutive even numbers to =540. let x = the middle number. (x-4) + (x-2) + X + (x+2)+ (x+4) = 540 ->5x=540 -> x=110, then angles are 106, 108, 110, 112, 114

Answer 7

Jim's pay- $320 Alicia's pay $480

side of square- 7cm

largest angle of pentagram- 112 degrees

Answer 8

do your own homework...