The percentage increase of a given quantity from 20 to 40 is 100%.
Original quantity = 20
New quantity = 40
In order to calculate the percentage increase, one had to subtract the original quantity from the new quantity and then divide the value by the original quantity. This will be:
= (New quantity - Original quantity) / Original quantity × 100
= (40 - 20) / 20 × 100
= 20/20 × 100
= 1 × 100
= 100%
Therefore, the percentage increase of the quantity from 20 to 40 is 100%.
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Answer:
1. 68/89
2. 46/267
Step-by-step explanation:
1. The total number of people in drama or athletics can be found by adding up all categories where a person fits at least one of the criteria:
51+11+12+15+108+7=204
Now we need to add up the total number of people in all categories:
51+11+12+15+108+7+63=267
Finally, we divide the total number of people in either drama or athletics by the total number of people in all categories:
204/267 = 68/89
2. The total number of people in athletics and drama can be found by adding up all categories where a person fits both criteria:
15+12=27
The total number of people in music and athletics can be found by adding up all categories where a person fits both criteria:
7+12=19
Now, we add both of these numbers together and put it all over the total number of people:
27+19=46
46/267
let's firstly convert the mixed fraction to improper fraction and then take it from there, keeping in mind that the whole is "x".
![\stackrel{mixed}{5\frac{5}{6}}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}x~~ = ~~5\frac{5}{6}\implies \cfrac{7}{3}x~~ = ~~\cfrac{35}{6}\implies 42x=105\implies x=\cfrac{105}{42} \\\\\\ x=\cfrac{21\cdot 5}{21\cdot 2}\implies x=\cfrac{21}{21}\cdot \cfrac{5}{2}\implies x=1\cdot \cfrac{5}{2}\implies x=2\frac{1}{2}](https://tex.z-dn.net/?f=%5Cstackrel%7Bmixed%7D%7B5%5Cfrac%7B5%7D%7B6%7D%7D%5Cimplies%20%5Ccfrac%7B5%5Ccdot%206%2B5%7D%7B6%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B35%7D%7B6%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B7%7D%7B3%7Dx~~%20%3D%20~~5%5Cfrac%7B5%7D%7B6%7D%5Cimplies%20%5Ccfrac%7B7%7D%7B3%7Dx~~%20%3D%20~~%5Ccfrac%7B35%7D%7B6%7D%5Cimplies%2042x%3D105%5Cimplies%20x%3D%5Ccfrac%7B105%7D%7B42%7D%20%5C%5C%5C%5C%5C%5C%20x%3D%5Ccfrac%7B21%5Ccdot%205%7D%7B21%5Ccdot%202%7D%5Cimplies%20x%3D%5Ccfrac%7B21%7D%7B21%7D%5Ccdot%20%5Ccfrac%7B5%7D%7B2%7D%5Cimplies%20x%3D1%5Ccdot%20%5Ccfrac%7B5%7D%7B2%7D%5Cimplies%20x%3D2%5Cfrac%7B1%7D%7B2%7D)
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
