not to be able to solve this maths problem for my Y7 DD?Plz help!!

[lupo5]

Here I am again..She is Y7 and this is really hard homework.She likes her maths and she solved all other problems but this is one of the hardest and I am totally confused.
If anyone can help plz,you would make our lives so much easier...
Question goes like this:

Two rectangular flower beds are made so that each has the same sized perimeter. The first has dimensions (3p+2) meters by (2p+1) meters.
The second has dimensions (p+8) meters by (2p+3).

A) Use this information to form an equation.
B) Solve this equation to find the perimeter of each flower bed.
C) State the dimensions of each flower bed.

Please please help.... thank you

2(3p+2)+2(2p+1)=2(P+8)+2(2p+3)

6p+4+4p+2=2p+16+4p+6
4p=16
P=4

Plug it in to the 2 equations to get the two perimeters.

And don't forget to include metres in the answer to c, instead of just giving a number. :)

Thank you all sooo much.You brought tears to my eyes.I gave her a nudge and I wont to see how she will do it herself.
She is finding it hard but I wont show her answers ,for sure,because in that way she wont learn.
Thank you soooooo much....

My brain hurts

Quite surprised at the number of adults on the thread not able to do this. We should all be able to do y7 maths!

Pud is correct.

Take your daughter (and yourself) through it logically.

The perimeter means all the way around, and you are told the flowerbeds have the same length - i.e. equal - perimeters even tho they are different shaped rectangles.

So the equation is: first flowerbed length = same as other flowerbed length.

Each rectangle bed has 2 sides one length, and 2 sides the other length (of course, as does any rectangle) so you x by 2 each measurement given, (as it is given one way - depth by width)

So put the lengths provided x 2 into your flowerbed equation and get answer to A:

2(3p+2)+2(2p +1) = 2(p+8) + 2(3p+2)

(Note the 2 outside the brackets means 2 x ie you multiply)

For avoidance of doubt, you ADD the width and depth not times (multiply/ x) them because we are working out total length of perimeter NOT the area of the beds, which you would x them for. (This is a deliberate test of your ability to make that leap as when you are given measurements as something 'by' something, you think of multiplying).

Moving to B, simplify the equation by working out what you can within it. Start with the 2x

2(3p+2)+2(2p +1) = 2(p+8) + 2(3p+2)
to get
6p + 6 + 4p + 2 = 2p + 16 + 6p + 4

then add up the numbers and 'p's:

10p + 8 = 8p + 20

Reduce it where you can -(remember this is an equation so it just needs to stay equal to be 'true' and is how you work out the values in it. You must do the same to both sides)
Here you can take out 8 and 8p to get:

2p = 12

Divide by 2 to get

p = 6

If p is 6 you apply this back to the original info:

3p+2 is one measurement so
(3 x 6) + 2 = 18 + 2
= 20

2p +1 = (2 x 6) + 1 = 12 + 1
= 13

So 20m by 13m is your answer to C for one of the flower beds.

There are 2 sides remember so multiply the sides by 2 to get answer to B for same bed: 40 + 26 = 66m

Apply all this to the other bed to get answers to B and C for the that bed. (I am late for a party!):
p+8
3p+2

She needs to think about what perimeter means and what same sized perimeter means. These are the keys to working out this question.

(2P+3)!=(3P+2) in this case (it would if P=1 but it doesn't).

Thank you all so much.She managed to work it out that a) part of the question with all of your help.I TRIED to read it to her that she understands that perimeter is same and with just a bit of idea she managed to work out a part of the question and other two were ok.
I really don't know what I would do without all of you.It is such a relief to know that there are such a nice people out there like yourselves,it doesn't happen often as you know ...
Thank you so much

Whois,you are lucky that you find maths easy...I do usually but my brain just stopped.Thankfully there are lots of kind people who helped us....

I think this is partly a comprehension issue. The first job in any 'wordy' question is to work out what they are saying:

"Two rectangular flower beds":
-We know there are 2.
-We know that each one is a rectangle in shape.

"are made so that each has the same sized perimeter.":
-'same' means 'equal'.
-We know they are talking about the perimeter, not the area.
-We know that the perimeter of a rectangle is made up of 2 x length, plus 2 x width.
-We know that when we're adding things together, it doesn't matter which order they go in (commutative operation), so we don't have to worry about which measurement is the length and which measurement is the width.

"The first has dimensions (3p+2) meters by (2p+1) meters.":
-The width/length of the first flower bed is 3p+2 and 2p+1

"The second has dimensions (p+8) meters by (2p+3).":
-The width/length of the second flower bed is p+8 and 2p+3.

Going back to the question parts:
"A) Use this information to form an equation.":

We know that the two perimeters are equal. We also know what the two measurements for the width and the length are of each flower bed, and that it doesn't matter which measurement is the width and which is the length. We also know that a rectangle has 4 sides, in 2 equal pairs. So:

2x(3p+2) + 2x(2p+1) = 2x(p+8) + 2x(2p+3)

Then we can tidy it up by firstly multiplying the brackets out, then adding all factors of the same type together:

6p + 4 + 4p + 2 = 2p + 16 + 4p + 6
10p + 6 = 6p + 22

"B) Solve this equation to find the perimeter of each flower bed.":

10p + 6 = 6p + 22

We need to get all the ps on one side, and the numbers on the other side, then divide by the amount of ps to find out what one p is equal to:

10p - 6p = 22 - 6
4p = 16
p = 4

Now that we know the value of 1p is 4, we can put that back into the equation in step A, to solve the perimeter, by using either flower bed one or flower bed two:

10p + 6 = (10 x 4) + 6 = 40 + 6 = 46
6p + 22 = (6 x 4) + 22 = 24 + 22 = 46

The perimeter is 46 metres.

"C) State the dimensions of each flower bed."

Use the p=4 from part B to work out the value of each dimension of each of the flower beds:

Flower bed one is (3p+2) metres by (2p+1) metres.

dimension A: (3 x 4) + 2 = 12 + 2 = 14 metres
dimension B: (2 x 4) + 1 = 9 metres

(Quick check: (14 x 2) + (9 x 2) = 28 + 18 = 46)

Flower bed two is (p+8) metres by (2p + 3) metres.

dimension A: 4 + 8 = 12 metres
dimension B: (2 x 4) + 3 = 11 metres

(Quick check: (12 x 2) + (11 x 2) = 24 + 22 = 46)

So, flower bed one is 14 metres by 9 metres and flower bed two is 12 metres by 11 metres.

Whois,you are lucky that you find maths easy

I'd rather be able to spell simple words than equations. Much more useful :-(

A) The perimeter of a rectangle is twice the length plus twice the width and the perimeter of both the flower beds is the same so the equation shows they are equal to each other:
2(3p+2)+2(2p+1)=2(p+8)+2(2p+3)

B) Simplify the equation then re-arrange it to solve it:
2(3p+2)+2(2p+1)=2(p+8)+2(2p+3)
6p+4+4p+2=2p+16+4p+6
10p+6=6p+22
10p=6p+22-6
10p=6p+16
10p-6p=16
4p=16
P=16/4
P=4

C) Use the value of P as 4 in the original dimensions given:
First flower bed
(3p+2)
3x4+2=12+2=14
(2p+1)
2x4+1=8+1=9
Dimensions are 14 by 9
Second flower bed
(P+8)
4+8=12
(2p+3)
2x4+3=8+3=11
Dimensions are 12 by 11

Final check that they equal each other:
2x14+2x9=28+18=46
2x12+2x11=24+22=46
Yep they are the same.

I love algebra that was fun :)

Hi realised after I had made a couple of typos earlier on in the equation (but my workings are core

Oops, meant to say 'my workings are correct which is the main thing in maths questions at school. But reworking it with the correct values then actually p = 4

Wow...I can't believe you wrote all that.THANK YOU SOOOOO MUCH.It made it so easy for me to actually explain that to her.
You all made my Sunday great.....Thank you soooo much.

Also get your daughter to draw rectangles, find rectangles and measure them. she can use mtric measures or lego bricks to do so. It doesn't matter but she will see that the opposite sides are the same same length. Look around the house, tables different sized books, cupboards etc