The price for an adult movie ticket is 1 1/3 more than a movie ticket for a child. Ines takes her daughter to the movie, buys a box of popcorn for $5.50, and spends $26.50. Write and solve an equation

Answer 1

So far we have two Expert answers to the problem. There is no fault in their math -- they just interpret the first sentence of the problem differently: "The price for an adult movie ticket is 1 1/3 more than a movie ticket for a child."

The first question is one of units: "1 1/3 more WHAT than a movie ticket for a child." You could say dollars or a proportion. One answer here assumes dollars ($1.33), and the other assumes a proportion (4/3) that is multiplied by the child price.

There is at least one more interpretation, having to do with the difference between saying "1 1/3 more than" and saying "1/3 more than".

For me, the moral of the story is that word problem writers should use the English phrases "more than" and "less than" *very* carefully, as they are ambiguous in certain contexts.

Answer 2

Start by assigning variables:

a = cost of adult ticket

c = cost of child ticket

p = cost of popcorn

We're told that the total cost of her trip - one adult ticket, one child ticket, and a box of popcorn - is $26.50.

total cost = 26.50 = a + c + p

We know cost of popcorn (p) is $5.50.

26.50 = a + c + 5.50

We're also given the relationship between the price of an adult ticket (a) and the price of a child ticket (c).

The price for an adult movie ticket (a) is (=) 1 1/3 more (x) than a movie ticket for a child (c).

a = 1 1/3 × c

1 1/3 can be rewritten as 4/3.

You can substitute this back into the first equation!

26.50 = a + c + 5.50

26.50 = (4/3 × c) + c + 5.50

26.50 = (7/3 × c) + 5.50

21.00 = 7/3 × c

c = 21.00 × (3/7) = $9.00

Now that we know the cost of the child ticket, we can substitute it back into the equation relating the adult and child ticket costs to figure out the adult ticket cost.

a = 4/3 × c

a = 4/3 × (9.00) = $12.00

Answer 3

According to the information given

Total cost of admission and popcorn = 26.50

Let Child Ticket = x

Let Adult Ticket = x + 1 1/3 = x + 4/3 = x + 1.33

Popcorn = $5.50

x + x + 1.33 + 5.50 = 26.50

Combine like terms, solve for x, recheck in the original equation

Give it a try