math problems i dont understand and i need to show the steps please help?

Question

13) It takes Stan 3 hours to mow the lawn and it takes Roger 2 hours. How long would it take them if they worked together?

17) 30 % of what number is 70?

25) The length of a rectangle is 5cm more than the width. The area is 150cm^2. Find the length of the width & Length.

27. A specialty food store mixes Brazil nuts and cashews to get misxed nuts that they sell for $5.00 per kilogram. If the Brazil nuts cost $4.50 per kilogram and the cashews cost $6.00 per kilogram, how many kilograms of each should be combined to give 30 kilograms of mixed nuts.

29) Frank needs 5 hours to rake his lawn. But when Sylvia helps him they can do the job in 3 hours. How long would it take sylvia to rake the lawn by herself?

33) The perimeter of a rectangle is 40cm, and the area is 64cm^2. Find the dimensions

35) I am thinking of two consecutive even integers. The sum of their squares is 340. What are the integers

Answer 1

It is nice that you included the numbers from your homework, too.

Can I do your laundry and mow the lawn while I am doing your homework?

:-)

Answer 2

Hi,

It sounds like you're having trouble putting words into numbers. I'll do one as an example.

25) The length of a rectangle is 5cm more than the width. The area is 150cm^2. Find the width & length.

Let:
width = w
length = l
area = A

Since the length is 5cm more than the width, take the width:

w

Then add 5cm to it

w + 5cm

and that's the length
l = w + 5cm

Also since we know that the area (of a rectangle) is

A = l x w

And we know that the area of THIS rectangle is 150 cm^2,

150cm^2 = l x w

Since we have two equations and two variables, it's usually easiest (at least for me) to substitute. It turns out that this particular equation is easier to show the calculation if we switch it around.

l = w + 5cm is the same as w = l - 5cm

Now plug it into into

150cm^2 = l x w

and you get

150cm^2 = l (l - 5cm)

which we can expand to form

150cm^2 = l^2 - (5cm)l

Then put in standard form:

l^2 - (5cm)l -150 = 0

and use the quadratic equation to solve (Sqrt means square root of the following parenthases).

l = [-(-5) +- Sqrt{(-5)^2 - 4(1)(-150)}]/2(1)

l = [5 +- Sqrt{(25) +600}]/2

l = [5 +- Sqrt{625}]/2

l = [5 +- 25]/2

l = 15cm or -10.

Since this is a geometric length, it doesn't make sense to have a negative number, and so we ignore that.

Since l = 15cm, and l x w= 150,

w = 150 / l = 150/15 = 10cm

as a check, plug your answer into the other equation to make sure that it makes sense.

QED

Hope that helps,
Matt

Answer 3

13. 1/T = 1/3 + 1/2 = 5/6
...T = 6/5 hours or 1h12m

17. x = 70/0.3 = 233 1/3

25. L = W + 5
...L * W = 150
...W(W + 5) = 150
...W² + 5W - 145 = 0
...(W + 15)(W - 10) = 0
...W = 10,-15
...Since you can't have a negative length, W = 10, L = 15

27. There are infinite solutions. If you want to maximize profit, you should only use Brazil nuts. To make a kilo cost exactly $5 (i.e. no profit):
...4.5C + 6(1 - C) = 5
...4.5C - 6C + 6 = 5
...1.5C = 1
...C = 2/3
...B = 1/3

To make 30 kilos, use 10 kilos Brazil and 20 kilos cashew.

29. 1/3 = 1/5 + 1/S
...1/S = 2/15
...S = 7.5 hours

33. 2W + 2L = 40 -> L = 20 - W
...W * L = 64
...W(20 - W) = 64
...W² - 20W + 64 = 0
...(W - 16)(W - 4) = 0
...W = 4, 16
The only solution that will work (i.e. to have a width that is 20 less than the length and an area of 64) is W = 4 and L = 16

35. x² + (x + 2)² = 340
...2x² + 4x + 4 = 340
...x² + 2x -168 = 0
...(x + 14)(x - 12) = 0
...x = 12, -14
There are two possible solutions: (12, 14) and (-12, -14).

Answer 4

13) Assuming that they start on the opposite ends of the lawn, it'll take them 1.5 hours (3/2) to mow the entire lawn.

17) 30% is 0.30. 0.30 times number x = 70. 0.30x=70. Solve for x. x=70/0.30. x is 233.333

25) area=length*width. let x be width. length is 5cm longer then width so then it's 5+x. 150=x(5+x). x^2+5x-150=0. use quadratic formula--x=-b+/-sqrt(b^2-4ac)all over 2a. x=10 and x=-15. Since x is width, it has to be positive, so the width is 10 and the length is 5+10 or 15.

27) let x be number of kilos for Brazil nuts and y be number of kilos for cashews. You need 30 kilos of nuts all together so x+y=30. You need the amounts of x and y such that, when there's 30 kilos, the price is $150. Since Brazil nuts is $4.50 and cashews are $6.00, the second equation is 4.5x+6y=150. You solve the first one for either x or y, but in our case we'll do x, but you can solve for either and end up with x=30-y. Substitute the x into the second equation to get 4.5(30-y)+6y=150. Solve for y (135-4.5y+6y=150 becomes 1.5y=15) and get y =10. Plug the y value back into your first equation (x=30-y) and get x=20. So you're mixing in 20 kilos of Brazil nuts at $4.50 a kilo ($90) and 10 kilos of cashews as $6.00 a kilo ($60) and get 30 kilos for $150.

29) I got the answer to number 13 by dividing the longer time by the shorter time. Assuming Sylvia is the shorter time doesn't give an answer that makes sense, so by assuming that she's the longer of the two, it's her time, x, divided by Frank's time 5 that gives us 3. Solve for x and we get x=15.

33) let w be width and l be length. 2w+2l=perimeter or 40. l*w=area or 64. Solving for l in the first we get l=20-w. Substitute l into the second equation, we get (20-w)w=64. 20w-w^2=64 is solved by the quadratic formula again. w=4 or w=16. Plug w as 4 back into l=20-w and we get l to be 16. Plug w as 16 into l=20-w and we get l to be 4. So it doesn't matter whether l is 16 or 4, just as long as w is the other.

35) let x and x+2 be the two consecutive even integers. the sum of their squares is x^2+(x+2)^2=340. solving for x we get 2x^2+4x-336=0. Again, using the quadratic formula, we get x=12 and x=-14. Trying both, we get both to be correct answers. The two integers can be 12 and 14 or -12 and -14.

Answer 5

1)W=3X , W =2Y WHERE X AND Y IS RATE OF EACH
THEN TX +TY =W , AS Y = 3X/2 THEN T( 5X/2)=W
T= 2/5 x W/X 2/5 x 3 = 6/5 h = 1.2h = 72 min.
2)70x100/30= 233 1/3
3)x(x+5)=150 then x^2 +5x -150=0 then w=5 m and l =10m
4)let x is weight of BN and y is weight of C. then 4.5 x + 6y =5 as x + y =1 then x = 2/3 and y =1/3
then 20kg and 10 kg resp.
4) it is as ist prob . and the result will be 7.5 h
5) x+y =20 and xy =64 then 4 and 16 m are the dimentions
6) x² + (x +2) ² = 340 then 2x ² +4x -336=0 then 12 and 14 are the two required numbers

Answer 6

33. Factors of 64//1/2 Perimeter
64*1//65
32*2//34
16*4//20
8*8//16

Perimeter = 2(l+w)
Area =l*w

16*4 = 64 cm^2
16+4+16+4 = 40 cm

Dimensions of Rectangle = 16 x 4 cm

Answer 7

17) It's your basic algebra problem with percents.
30% of what number (in this case we'll use X) equals 70
or
.30X = 70 and then just solve for X