Question

A charity bingo game costs $2 per round and has a $13 entry fee for an adult. It costs $3 per round and a $10 entry fee for a child. For how many rounds of bingo are the costs the same for an adult and a child?

Answer 1

:a 2

b 3

c 4

d 5

Answer :b. 3

Step-by-step explanation:

We can derive our equation by determining one for the adult and one for the child

Let x = number of rounds

Adult (A):

A = 2x + 13

Child (C):

C = 3x + 10

The question is at how many rounds will these two equations be equal? In other words, when will A = C? So we just combine the equations:

    A    =    C

2x + 13 = 3x + 10                 Subtract both sides by 10

2x + 13 - 10 = 3x + 10 - 10

2x + 3 = 3x                         Subtract both sides by 2x

2x - 2x + 3 = 3x - 2x

3 = x

So the answer is 3 rounds.

Let's check:

A = 2x + 13              C = 3x + 10

 = 2(3) + 13               = 3(3) + 10

 = 6 + 13                   = 9 + 10

 = $19                       = $19