Melissa, dale, and brian sent a total of 96 text messages over their cell phones during the weekend. brian sent 6 more messages than melissa. dale sent 4 times as many messages as brian. how many messages did they each send?

Melissa sent 11 messages

Dale sent 68 messages

Brian sent 17 messages

Step-by-step explanation:

Let m = number of messages sent by Melissa

Let d = number of messages sent by Dale

Let b = number of messages sent by Brian

Melissa, Dale, and Brian sent a total of 96 text messages over their cell phones during the weekend. This means that

m + d + b = 96 - - - - - - 1

Brian sent 6 more messages than Melissa. This means

b = m + 6 - - - - - - 2

Dale sent 4 times as many messages as Brian. It means

d = 4b

Substituting m = b - 6 and d = 4b into equation 1, it becomes

b - 6 + 4b + b = 96

6b = 96 + 6 = 102

b = 102/6 = 17

d = 4b = 4× 17 = 68

m = b - 6 = 17 - 6 = 11

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.