Kira john and ryan sent a total of 112 text messages during the weekend. kira sent 8 fewer messages than ryan. john sent 4 times as many messages as ryan. how many messages did they each send?

The message send by each person

Message sent by Ryan is 20

Message sent by Kira is 12

Message send by John is 80

Step-by-step explanation:

Given as :

The total number of messages sent y three people Kira , John , Ryan = 112

Kira sent 8 fewer messages than Ryan.

John sent 4 times as many messages as Ryan.

Let The message sent by Kira = K

The message sent by John = J

The message sent by  Ryan = R

So, According to question

K + J + R = 112

And K = R -8

And  J = 4 × R

So, ( R - 8 ) + 4 × R + R = 112

or , R + 4 R + R = 112 + 8

Or,  6 R = 120

or , R =

I.e R = 20

So, Message sent by Ryan = R = 20

Similarly K = R - 8

I.e K = 20 - 8 = 12

Or , K = 12

So, Message sent by Kira = K = 12

And J = 4 × R

I.e J = 4 × 20

or, J = 80

So, the message send by John = J = 80

Hence The message send by each person

Message sent by Ryan is 20

Message sent by Kira is 12

Message send by John is 80 Answer

The number of messages sent by Ryan is 20 and by Kira is 12 and by John is 80.

Step-by-step explanation:

Given,

Total number of messages = 112

Solution,

Let the number  of messages sent by Ryan be x.

So the number  of messages sent by Kira =

And the number  of messages sent by John = 4x

The total number of messages is sum of messages sent by all of them.

Total number of messages = number  of messages sent by Ryan +  number  of messages sent by Kira + number  of messages sent by John

Which is represented by the equation as;

Hence the number of messages sent by Ryan is 20 and by Kira is 12 and by John is 80.

tell you what. i'll find the length of the medians and you can fill in the blanks where they belong.

br

b = (2a,0)

r = (a/2,b/2) remember these things are medians. they go to the 1/2 way point of the line opposite the vertex they face.

br^2 =   (2a - a/2)^2 + (0 - b/2)^2

br^2 = (3/2 a) ^2 + b^2 / 4

br^2 = 9/4 a^2 + b^2 / 4   we need to find some relationship between a and b.

let's try ab = bc  

ab = 2a

bc = (2a - a)^2 + (b - 0)^2

bc = sqrt(a^2 + b^2)

ab = bc

2a = sqrt(a^2 + b^2) square both sides.

4a^2 = a^2 + b^2 subtract a^2 from both sides.

sqrt(3a^2) = sqrt(b^2)

sqrt(3)a = b

let's put b into br^2

br^2 = 9/4 a^2 + 3b^2 / 4

br^2 = 12 a^2 / 4

br^2 = 3a^2 

br = sqrt(3) * a

cp

c = (a,b) ; p = (a,0) this is another application of the distance formula, and it is a good one.

cp^2 = (a - a)^2 + (b - 0)^2

cp^2 = 0 + b^2

cp^2 = b^2 which you can see from the diagram. 

cp = sqrt(b^2)

cp = b but b = sqrt(3) * a 

cp = sqrt(3)*a

aq

a = (0,0)

q = (3/2) a, b/2

aq^2 = (3a/2 -0)^2 + (b/2 - 0)^2

aq^2 = 9a^2/4 + b^2/4

but b = sqrt(3) * a 

aq^2 = 9a^2 / 4 + (sqrt(3)*a)^2 /4

aq^2 = 9 a^2/ 4 + 3 a^2 / 4

aq^2 = 12 a^2/4

aq^2 = 3 a^2

aq = (sqrt  3) * a which agrees with the other two.

y=20x

: )

hope this