# The play at the theater charges $7 for adults, $5 for school-age children, and $3 for babies?

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The play at the theater charges $7 for adults, $5 for school-age children, and $3 for babies. A group of people went to see the play. There were the same number of school-age children as babies and the number of adults was the same as school-age children and babies combined. If the group paid $1562, how many babies were there?

The play at the theater charges $7 for adults, $5 for school-age children, and $3 for babies. A group of people went to see the play. There were the same number of school-age children as babies and the number of adults was the same as school-age children and babies combined. If the group paid $1562, how many babies were there?

##### 2 Answers

There were 71 babies.

#### Explanation:

First define some variables:

Let

Let

Let

Now write some equations.

(1) Money:

(2) Children vs. babies:

(3) Adults vs. Children&Babies:

Subbing (2) into (3) we get that

Subbing (2) and (4) into (1) we get:

If

Subbing these values back into (1) confirms that this solution works.

Since

#### Explanation:

Problems like this can be confusing for two reasons:

- It's hard to find a good way to express all those amounts
- There are two kinds of data to consider:

. . . ~ The NUMBER of tickets of each type that were sold

. . . ~ The monetary VALUE of each type of ticket

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**First find a way to express the NUMBER sold of each type of ticket**

Let

Babies' tickets . . . . . . . . . . . .

Same number . . . . . . . . . . . ..

The combined number . . .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**Now find a way to express the VALUE of the tickets sold**

~ ~ ~ ~ ~ ~ ~ ~ ~

**Now you can set up the equation**

[babies' value] plus [children's value] plus [adults' value] = $1562

[ . . . . .

Solve for

1) Clear the parentheses by distributing the 7

2) Combine like terms

3) Divide both sides by 22 to isolate

Answer:

There were 71 babies

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**Check:**

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