Your consecutive numbers are 52, 53, 54, 55, and 56.
I found an easy way to determine this; Divide 270 by 5 to get close to the consecutive numbers, since they are almost (number) x 5.
52 + 53 = 105,
105 + 54 = 159
159 + 55 = 214
214 + 56 = 270.
Hope this helps!
Using a proportional relationship, we have that:
- The table is completed as follows: x = 4, y = 192; x = 6, y = 288; x = 9; y = 432;
- 6 boxes are not enough for 300 pencils, 7 are needed.
<h3>What is a direct proportional relationship?</h3>
A direct proportional relationship is a function in which the output variable is found with the multiplication of the input variable and the constant of proportionality k, as follows:
y = kx.
From the table in this problem, the constant is given as follows:
k = 240/5 = 48/1 = 48.
Hence the relationship is:
y = 48x.
Then:
- When x = 4, y = 48(4) = 192.
- When x = 6, y = 48(6) = 288.
- When x = 9, y = 48(9) = 432.
For 300 pencils, the number of boxes is given by:
48x = 300
x = 300/48
x = 6.25.
There are not decimal parts of a box, a complete box is needed, hence 7 boxes are needed, meaning that 6 boxes are not enough for 300 pencils.
More can be learned about proportional relationships at brainly.com/question/10424180
#SPJ1
![\dfrac{5 \textrm{ wings}}{4 \textrm{ dollars}} = \dfrac 5 4 \textrm{ wings per dollar}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B5%20%5Ctextrm%7B%20wings%7D%7D%7B4%20%5Ctextrm%7B%20dollars%7D%7D%20%3D%20%5Cdfrac%205%204%20%5Ctextrm%7B%20wings%20per%20dollar%7D)
We could write the 5/4 various ways but I think the reduced improper fraction is simplest.
Length of blue cloth is 60 inches , length of gold cloth is 48 inches and length of white cloth is 72 inches.
<u>a.</u>
As, the length of all pieces are equal, so for getting the greatest possible length of the pieces, we need to find <u>GCF(greatest common factor) of 60, 48 and 72. </u>
First we will factor out all three numbers completely......
![60=2*2*3*5\\ \\ 48=2*2*2*2*3\\ \\ 72=2*2*2*3*3](https://tex.z-dn.net/?f=60%3D2%2A2%2A3%2A5%5C%5C%20%5C%5C%2048%3D2%2A2%2A2%2A2%2A3%5C%5C%20%5C%5C%2072%3D2%2A2%2A2%2A3%2A3)
The common factors are: 2, 2 and 3
Thus the GCF ![= 2*2*3=12](https://tex.z-dn.net/?f=%3D%202%2A2%2A3%3D12)
So, the greatest possible length of the pieces without having any cloth left over will be 12 inches.
<u>b. </u>
For finding the number of pieces for each color cloth, we will just <u>divide the length of each cloth by 12</u>. So...
Number of pieces for blue cloth ![=\frac{60}{12}=5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B60%7D%7B12%7D%3D5)
Number of pieces for gold cloth
and
Number of pieces for white cloth ![=\frac{72}{12}=6](https://tex.z-dn.net/?f=%3D%5Cfrac%7B72%7D%7B12%7D%3D6)