Karen and Dale and Tom sent a total of 84 messages during the weekend. Dale sent six fewer messages and Karen and Tom sent four times as many as Karen. How many did they send each.

Karen: 15; Dale: 9; Tom: 60

Step-by-step explanation:

"Karen and Dale and Tom sent a total of 84 messages during the weekend."

k + d + t = 84

"Dale sent six fewer messages than Karen"

d = k - 6

"Tom sent four times as many as Karen."

t = 4k

Substitute k - 6 for d and 4k for t in the first equation.

k + d + t = 84

k + k - 6 + 4k = 84

6k - 6 = 84

6k = 90

k = 15

d = k - 6 = 16 - 6 = 9

t = 4k = 4(15) = 60

Karen: 15; Dale: 9; Tom: 60

what is the original number? you forgot to add it.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)