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