Here is the latest POTW (#10):
Thursday, November 5, 2015
POTW #10 (AND #9 Solution)
I really liked how last week's POTW challneged students more than some of the previous questions. Please see one way below to find the correct answer of $2.80 PER HOUR increase in wage. Remember to answer the specific question asked, i.e. rate of change in his hourly wage!
Here is the latest POTW (#10):
Here is the latest POTW (#10):
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Since the wire is 60 cm and the ratio is 3:2 for the two parts the parts are basically 3/5 and 2/5 of the wire respectively.
ReplyDelete3/5 of 60=36 cm
2/5 of 60=24 cm
Since they are bent into squares to find out the side lengths you have to divide by 4.
36 divided by 4=9 cm 9x9=81 cm 2
24 divided by 4=6 cm 6x6=36 cm 2
81:36 is the ratio but it can be reduced. The GCF of 81 and 36 is 9 so you can divide each number by 9 to reduce the ratio. Therefore, the ratio of the area of the larger square to the smaller square is 9:4.
To solve the question I first tired to find how much wire is cut. A ratio of 3:2 for cut wire would be one piece 36 cm and one piece 24 cm. Since the wire is bent into squares that means I will divide each one by 4 to get each side length. Then I got a side length of 9 for the first one and 6 for the second one. This means the ratio is still 3:2
ReplyDeleteIf the wire is 60cm long, and the ratios are 3:2, the total is 5.
ReplyDelete60 ÷ 5 = 12
Now that I had 1 part of 60, I divided it by the ratios.
12 x 3 = 36cm (3 length part)
12 x 2 = 24cm (2 length part)
36 + 24 =60
To double check I got the right lengths, I add the up again to see if they got 60cm. (the total of the wire)
Since a square had 4 sides that are all equal, I knew I had to divide the lengths of both parts by 4.
36 ÷ 4 = 9 (base & height)
24 ÷ 4 = 6 (base & height)
The formula to find area of a parallelogram is base x height, so that is what I did for the square.
3 part: 9 x 9 = 81cm2
2 part: 6 x 6 = 36cm2
That gives the area ratio of the two formed squares 81:36
To solve this problem, first I found the ratio of 3 : 2. To do so, I added the two numbers together (3+2) and got 5. Then, I divided 60 by 5, to result in 12. To find what the values on each side of the colon were, I multiplied them by twelve:
ReplyDelete3 x 12 = 36
2 x 12 = 24
To double check, I added them together and saw that they equalled 60:
36 + 24 = 60
Then, I found the area of each square, by divided each number by 4. This was because a square has 4 equal parts, thus divided a number by 4 will result in the length of each side:
36 ÷ 4 = 9
24 ÷ 4 = 6
Next, found the area by multiplying each number by itself:
9 x 9 = 81
6 x 6 = 36
So, the area of the larger square is 81 squared centimetres, and the area of the smaller square is 36 squared centimetres. Therefore, the ratio of the two areas is 81 : 36 or 4 : 9 (reduced).
First, you must find how long each piece of wire is after its cut:
ReplyDeleteYou don't know how much "1" is, so lets assume that it's 10. 30:20 is now the ratio. However, that equals to 50. Now all I did was to add equal amounts to both numbers, so I got 35cm and 25cm. Those are the wire lengths.
Now you make the wire pieces into squares, and the sides must be equal or its not a square. So all I did is divide the wire length with the amount of sides/edges, which would be: 35/4 = 8.75. The side lengths are all 8.75 cm. To get the area, just times 8.75 by 8.75: 8.75*8.75 = 76.5625. I will round this number until it's not a decimal, or it will be to confusing: 77 cm2.
Now for the other wire: 25/4 = 6.25*6.25 = 39.0625 rounded is 39 cm2.
Find the ratio of the areas: 77 to 39 is almost 1:2. It's 0.5 away, but I don't know where to put that decimal so I guess this is my answer:
The ratio of the area of the larger square to the smaller square is 1:2.
I know that the wire is 60cm with a ratio of 3:2 so the wires must be 36 and 24.
ReplyDeleteTo get the length of the sides of the squares I must divide each number by 4.
36÷4=9 and 24÷4=6
and if i use the formula for area (bxh) I get 81cm2 and 36cm2
The ratio of the areas in simplest form is 9:4
First I did 60/5 because 3+2=5. 60/5=12. I know each piece is 12 cm long. 12*3=36. The perimeter of the larger square is 36 cm. Then I did 12*2=24. Therefore the perimeter of the smaller square is 24. In order to check I did 36+24=60 so I knew I was most likely correct. Then I divided 36 by 4 to find the length of one side. 36/4=9 and since I know the sides of a square are all the same length I did 9*9=81 so the area of the larger one is 81 cm2. Then I went ahead and divided 24 by 4 and got 6. 6*6=36. The area of the smaller square is 36cm2. The ratio of the larger square to the smaller square is 81:36 or 9:4.
ReplyDeleteWire = 60 cm
ReplyDeletePart A:Part B = 3:2
A=3/5 B=2/5
P(Square)=Side*4
Side=P/4
A=((3/5*60)/4)^2 B=((2/5*60)/4)^2
A=81 cm2 B=36 cm2
A:B = 81:36
= 9:4
The ration of the area of the larger square to the smaller square is 9:4.
To find the area and the ratio of the squares, the first thing I need to do is calculate the ratio of 2 pieces of wire: 3:2.
ReplyDeleteThe wire is 60cm, so:
3:2 = ⅗ to ⅖
Then I divided 60cm by 5 = 12cm
so 3 X 12 = 36 and 2 X 12 = 24
3:2 = 36:24
So one peice of wire is 36, and one is 24.
A square has 4 equal sides,, so I divide each number by 4:
36 divided by 4 = 9cm per side
24 divided by 4 = 6cm per side
Area = Length X Width
So 9cm X 9cm (Let’s call this square A) = 81cm squared
And 6cm X6cm (Let’s call this square B) = 36cm squared
So I have the areas of the squares, now I need to put in the ratio:
Ratio = 81:36, but that can be divided. Both numbers can be divided by 9, so I divide:
81 divided by 9 = 9
36 divided by 9 = 4
So the ratio between the larger and smaller squares is 9:4
To solve this question I first divide 60 by two to get 30. Then I slowly move up to find numbers 36 and 24. I then divided it by 4 since there are 4 sides on a square. Thus I got 9 and 6. Then to get the area of each square I used the formula of LxW=A. Thus I got 81:36. Then I simply just found the lowest common factor (9) and divided the two areas to get it reduced. Thus I got 9:4. The ratio between the area of the larger square and the smaller square is 9:4
ReplyDeleteThe ratio from the larger square to the smaller square is 9:4.
ReplyDeleteHow I answered this question was that I first saw that the ratio for the cut wires was 3:2. So I added 3 and 2 to get 5. Then I did 60 / 5 to get 12. That means that each wire is 12 cm long. So then I multiplied 3 by 12 and 2 by 12 to get 36 and 24. This was the perimetre of both of the squares but we need to find area. So I first divide 36 by 4 to get 9. That was the length for all 4 sides of that square. So then I did 9 x 9 to get the area which was 81cm squared. Then I did the same thing to the next square. 12 / 4 = 6. 6 x 6 = 36cm squared. So that ratio is 81 : 36. But we want to reduce it to the lowest we can so I looked for the LCM of 81 and 36 which is 9. so I did 81 / 9 to get 9 and 36 / 9 is 4. So 9:6 is it reduced.
I meant 9:4
DeletePOTW 10
ReplyDeleteQ: There is a 60cm piece of wire. It is cut into 2 pieces with a 3:2 ratios. The2 wires are then bent into squares. What is the ratio between the larger square and smaller square area?
Area: TO start off I calculated the length of each wire cut. 3:2 is equivalent to 3/5 and 2/5. 3/5 of 60 is 36, and 2/5 out of 60 is equal to 24. I then divided each wire by four, as a square has 4 sides, thus I got 9 and 6. Next, I used the formula length times width to get the area of the larger square and smaller square.
Larger Square: 9x9= 81
Smaller square: 6x6=36
The common factor of these areas is 9. I then divided the 2 areas by 9, thus I got the reduced ratio of 9:4.
A 3:2 ratio can be written as fractions of the whole, so 3/5 and 2/5. Therefore, I found 3/5 of 60cm, which would be 36 cm, and 2/5 of 60cm is 24cm. So, 36 cm makes one square, and 24 cm makes the other. Since I need to find the areas of the squares to compare them, I find the side lengths.
ReplyDelete36/4(number of sides in a square)= 9cm side lengths
24/4(number of sides in a square)= 6cm side lengths
To find the area, I need to multiply length by width, but since they're squares, the length and width are the same.
9*9= 81cm squared
6*6= 36cm squared
So the ratio of the area of the larger square to the smaller square is 81:36. But this ratio can be reduced, as both 81 and 36 share common factors. The largest one they have in common is 9, so I divide both numbers by 9 to give me the reduced ratio.
81/9= 9
36/9= 4
Therefore the ratio between the areas of the two squares is 9:4.
2 + 3 = 5
ReplyDelete60 / 5 = 12
12 x 3 = 36
12 x 2 = 24
36 / 4 = 9
24 / 4 = 6
9 x 9 = 81
6 x 6 = 36
81 / 9 = 9
36 / 9 = 4
The ratio is 9:4
To get this I first had to find what the total amount of fractions would be, and for that I got 5 (2 + 3) and with that I could find the 1:1 ratio, which is 12 (60 / 5). So after that I went on to find the total amount of wire cut for each piece cut for which I got 36 and 24 (12 x 3)(12 x 2).so then I went on a process to find the area for which I got 81cm2 and 36cm2 (36 / 4 = 9, 24 / 4 = 6, 9 x 9 = 81, 6 x 6 = 36). And then I decreased it by dividing it by 9 for both sides from which I got a ratio of 9:4.
First I figured out what the length of each wire was. To do this I divided 60 into 3:2 to get 36:24. These are the lengths of the two wires. Then I divide both numbers by 4 to get each side. That number is the length and the width, so multiply it by itself to get the area of the suare. I then did this to both squares:
ReplyDeleteSquare 1:
36/4=9
9x9=81
Square 2:
24/4=6
6x6=36
The ratio is 81:36, but that can be reduced, so the reduced answer is 9:4. (It is reduced by 9.)