Math problems.. i really dont get this. ?

Question

okay.. im not trying to find my way out of this.
i really dont get it.
ive tried it over and over.

1. the lengths of the sides of a triangle are consecutive even integers. Find the length of the longest side if it is 22 units shorer than the perimeter.

2. the length of a rectangle is twice the width. the peremiter is 84 cm more than the width. Find the rectangles dimensions.

3. Mei's salary starts at $16,000 per year with annual raises of $1500. Janet's starting salary os $19,300 with annual raises of $950. After how many years will the two women be earning the same salary?

please help.

Answer 1

1~~~~

ok, let x = longest side, and p = perimeter

therefore, x + 22 = p (because the longest side is 22 units shorter than the perimeter)

also, the sides of the triangle are:

x, x-2, and x-4 (because they are even consecutive numbers)

p = sum of the lengths of the three sides

p = (x) + (x - 2) + (x - 4)

p = x + x - 2 + x - 4

p = 3x - 6



We showed at the start that p = x + 22. So, if p = x + 22, and p also = 3(x - 2), then we can say that x + 22 = 3x - 6

3x - 6 = x + 22

subtract x from both sides

2x - 6 = 22

add 6 to both sides

2x = 28

divide both sides by 2

x = 14

_________________________

2~~~~

this is a similar question,

w + 84 = p

l = 2w
p = 2l + 2w

replace l with 2w

p = 2(2w) + 2w

before we said that p = w + 84, so

2(2w) + 2w = w + 84

4w + 2w = w + 84

6w = w + 84

subtract w from both sides

5w = 84

w = 16.8

l = 2w

l = 33.6

so w = 16.8 and l = 33.6

_________________________

3~~~~

Ok, so after y amount of years m (mei's salary) will equal j (janet's salary)

currently:
m = 16 000
j = 19 300

m + y(1500) = j + y(950)
16 000 + 1500y = 19 300 + 950y
1500y - 950y = 19 300 - 16 000
550y = 3300
y = 3300/550
y = 6

so the answer is after six years

:)

Answer 2

(!) Let the lengths of the sides of the triangle be x.x+2 and x+4 units respectively. Therefore,the perimeter of the triangle is 3x+6.Now according to the problem 3x+6=x+4+22 =>3x-x=22-6=16 =>x=8 units. So,length of the longest side is 8+4 or 12 units. ans. (2) Let the width of the rectangle be x cm. So its length is 2x cm.Therefore its perimeter is 2(x+2x) or 6x .Now according to the problem , 6x=x+84 => 6x-x=84 =>5x=84 =>x=84/5=16.8 cm Therefore the width of the rectangle is 16.8 cm and its length is 2X16.8=33.6 cm. ans. (3)The difference in starting salaries is $ 3300 ,The difference in annual raise is $550 Therefore the no.of years required to level their salaries is (3300/550)=6 years,

Answer 3

OK, here's the first one.

Let the length of the longest side be x.
Since the side lengths are consecutive even integers, that means the other two sides must be (x-2) and (x-4).
The perimeter is therefore x + (x-2) + (x-4), which equals 3x-6.
We are told that (3x-6) - 22 = x
Moving the variables to the left side and numbers to the right, this turns into:
2x = 28
Therefore, x = 14

The length of the longest side is 14.

Answer 4

1)
Let x,y,z be the sides of the triangle

Consecutive even integers:
x=y+2~~~~x is longest
y=x-2##EQ.1##

y=z+2~~~~z is shortest
z=y-2##EQ.2##

Length of longest side, 22 units shorter than Perimeter:
x+22=Perimeter
x+22=x+y+z##EQ.3##

Sub the equations together, (EQ. 1,2,3)
x+22=x+(x-2)+(y-2)
x+22=x+(x-2)+((x-2)-2)
x+22=x+x-2+(x-4)
x+22=2x-2+x-4
x+22=3x-6
2x=28
x=14

sub x=14 back into EQ. 1,2
y=x-2
y=14-2
y=12

z=y-2
z=12-2
z=10

x=14, y=12, z=10


2)
Let L be length, let W be width

Length is twice the width:
L=2W##EQ.1##
Perimeter is 84 cm more than width
P= 2L+2W
(2L+2W) = W +84##EQ.2##

sub the 2 equations, EQ.1, 2
(2(2W)+2W) = W + 84
4W+2W=W+84
5W=84
W=16.8

L=2W
L=2(16.8)
L=33.6

W=16.8cm, L=33.6cm


3)
Let F be the final salary of both women
Let Y be number of years

Mei:
F = 16,000 + Y(1500)

Janet:
F = 19,300 + Y(950)

Since they will have the same salary after Y years, we can equate the 2 equations:

16,000 + Y(1500) = 19,300 + Y(950)

550Y = 3,300

Y=6

6 years

Answer 5

For the second, L = 2*W Perimeter = 2*L + 2*W, this = W + 84; From the perimeter relation you get 2*L +2*W = (W + 84); from the first you have L = 2*W. Put that in in for L to get

4*W +2*W = (W + 84) solve for W. Once you have W, get L from L=2*W

Let n = no of years. Men's salary is 16000+n*1500; Janets is 19300+n*950. Set these to be equal: 16000+n*1500 = 19300+n*950
solve for n

Answer 6

since you have got the first one here;s the second
the width is x
so length is 2x
so perimeter is 2x +2x +x +x=6x
but perimeter is 84 more than the width so 6x =84 + x
6x -x=84
5x=84
x=84/5
x=16.8
width= 16.8units
length=33.6units

Answer 7

2) The dimensions are 16.8cm x 33.6cm...using zebra crossing method.

3) At 6 years they will become equal