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 mes

Question

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?

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Mackenzie 1 week 2021-09-09T13:54:08+00:00 2 Answers 0

Answers ( )

    0
    2021-09-09T13:55:34+00:00

    Answer:

    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 = \frac{120}{6}

    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

    0
    2021-09-09T13:55:58+00:00

    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 = (x-8)

    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;

    112=x+(x-8)+4x\\112=x+x+4x-8\\6x=112+8\\6x=120\\\\x=\frac{120}{6}=20

    x=20\\\therefore x-8=20-8=12\\\therefore4x=4\times20=80

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

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