Question

Karen, Lamar, and John sent a total of 160 text messages over their cell phones during the weekend. John sent 4 times as many messages as Lamar. Lamar sent 10 fewer messages than Karen. How many messages did they each send?

Answer 1

Karen= 35 messages

Lamar= 25 messages

John= 100 messages

Explanation:

Let the number of messages Karen, Lamar and John send be K, L and J messages respectively.

`\textcolor{steelblue}{\text{\textcircled{2} Form equations with given information}}`

K +L +J= 160 -----(1)

J= 4L -----(2)

L= K -10 -----(3)

`\textcolor{steelblue}{\text{\textcircled{3} Solve by substitution}}`

Substitute (3) into (2):

J= 4(K -10)

J= 4K -40 -----(4)

Substitute (3) and (4) into (1):

K +(K -10) +(4K -40)= 160

Simplify:

6K -50= 160

6K= 160 +50

6K= 210

Divide both sides by 6:

K= 210 ÷6

K= 35

Substitute K= 35 into (3):

L= 35 -10

L= 25

Substitute L= 25 into (2):

J= 4(25)

J= 100

`\textcolor{steelblue}{\text{\textcircled{4} Concluding statement}}`

Thus Karen, Lamar and John sent 35, 25 and 100 messages respectively.