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?
a 2
b 3
c 4
d 5

Answer 1

For this case we have to:

x: Be the variable that represents the number of adult rounds

y: Be the variable that represents the number of rounds of children

We want to know for what amount of rounds bingo costs are the same for adults and children.

Adult costs = 2x + 13

Child costs = 3y + 10

Matching:

$2x + 13 = 3y + 10$

We want the same number of rounds, x = y:

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

Thus, for 3 rounds the costs are the same.

Answer:

3

Answer 2

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