So, let's see, the point say P, is 3/4 of the way from R to S, namely, if we split the segment RS into 4 pieces, from R to P, or RP will take 3 of those quarters, and from P to S, or PS, will take one of those quarters, check the picture below.
so the RP section is at a ratio of 3, whilst the PS section is at a ratio of 1.
![\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ R(1,2)\qquad S(6,7)\qquad \qquad 3:1 \\\\\\ \cfrac{R\underline{P}}{\underline{P} S} = \cfrac{3}{1}\implies \cfrac{R}{S} = \cfrac{3}{1}\implies 1R=3S\implies 1(1,2)=3(6,7)\\\\ -------------------------------](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Binternal%20division%20of%20a%20line%20segment%7D%0A%5C%5C%5C%5C%5C%5C%0AR%281%2C2%29%5Cqquad%20S%286%2C7%29%5Cqquad%0A%5Cqquad%203%3A1%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7BR%5Cunderline%7BP%7D%7D%7B%5Cunderline%7BP%7D%20S%7D%20%3D%20%5Ccfrac%7B3%7D%7B1%7D%5Cimplies%20%5Ccfrac%7BR%7D%7BS%7D%20%3D%20%5Ccfrac%7B3%7D%7B1%7D%5Cimplies%201R%3D3S%5Cimplies%201%281%2C2%29%3D3%286%2C7%29%5C%5C%5C%5C%0A-------------------------------)
![\bf { P=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\ -------------------------------\\\\ P=\left(\cfrac{(1\cdot 1)+(3\cdot 6)}{3+1}\quad ,\quad \cfrac{(1\cdot 2)+(3\cdot 7)}{3+1}\right) \\\\\\ P=\left( \qquad \qquad ,\cfrac{2+21}{4} \right)\implies P=\left( \qquad \qquad ,\cfrac{23}{4} \right)](https://tex.z-dn.net/?f=%5Cbf%20%7B%20P%3D%5Cleft%28%5Ccfrac%7B%5Ctextit%7Bsum%20of%20%22x%22%20values%7D%7D%7B%5Ctextit%7Bsum%20of%20ratios%7D%7D%5Cquad%20%2C%5Cquad%20%5Ccfrac%7B%5Ctextit%7Bsum%20of%20%22y%22%20values%7D%7D%7B%5Ctextit%7Bsum%20of%20ratios%7D%7D%5Cright%29%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0AP%3D%5Cleft%28%5Ccfrac%7B%281%5Ccdot%201%29%2B%283%5Ccdot%206%29%7D%7B3%2B1%7D%5Cquad%20%2C%5Cquad%20%5Ccfrac%7B%281%5Ccdot%202%29%2B%283%5Ccdot%207%29%7D%7B3%2B1%7D%5Cright%29%0A%5C%5C%5C%5C%5C%5C%0AP%3D%5Cleft%28%20%5Cqquad%20%5Cqquad%20%2C%5Ccfrac%7B2%2B21%7D%7B4%7D%20%5Cright%29%5Cimplies%20P%3D%5Cleft%28%20%5Cqquad%20%5Cqquad%20%2C%5Ccfrac%7B23%7D%7B4%7D%20%5Cright%29)
and that's the y-coordinate for the point P.
The amount of the mortgage is
89,400 - 20% of 89400
Answer:
Children: $13
Adults: $18
Step-by-step explanation:
Well for both sets we can set up the following system of equations,
![\left \{ {{3a + 4c = 106} \atop {2a + 3c = 75}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B3a%20%2B%204c%20%3D%20106%7D%20%5Catop%20%7B2a%20%2B%203c%20%3D%2075%7D%7D%20%5Cright.)
So first we need to solve for a in the first equation.
3a + 4c = 106
-4c to both sides
3a = -4c + 106
Divide 3 by both sides
<u>a = -4/3c + 35 1/3</u>
Now we plug in that a for a in 2a + 3c = 75.
2(-4/3c + 35 1/3) + 3c = 75
-8/3c + 70 2/3 + 3c = 75
Combine like terms
1/3c + 70 2/3 = 75
-70 2/3 to both sides
1/3c = 4 1/3
Divide 1/3 to both sides
c = 13
Now we can plug in 13 for c in 3a + 4c = 106,
3a + 4(13) = 106
3a + 52 = 106
-52 to both sides
3a = 54
Divide 3 by both sides.
a = 18
<em>Thus,</em>
<em>an adult ticket is $18 and a children's ticket is $13.</em>
<em />
<em>Hope this helps :)</em>
The mean you have to add up your numbers first then divide them by the amount of numbers you have .ex. 1+2+3 is 6 then divide so 6÷3 =3
Median is the middle number in list. So put them in order then muddle number is your median. If you have two numbers left add them and divide by 2. That will be your median.