In the last election, Candidate C received 15,000 fewer votes than candidate B. If a total of 109,000 votes were cast, how many votes did candidate B receive? What is the equation for this problem and what is the answer to it?

B receives 62000 votes

C receives 47000 votes

Step-by-step explanation:

Let C be the vote for candidate C

Let B be the vote for candidates D

Let the total vote be T. Therefore,

C + B = T (1)

But C receives 15000 votes fewer than B ie

C = B —15000 (2)

Total votes, T = 109000

Substituting the value of C and T into equation 1

C + B = T

B — 15000 + B = 109000

Collect like terms

B + B = 109000 + 15000

2B = 124000

Divide both side by the coefficient B i.e 2

B = 124000/2

B = 62000

Putting the value of B into equation 2;

C = B —15000

But B = 62000

C = 62000 — 15000

C = 47000

B receives 62000 votes

C receives 47000 votes

∠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.