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A movie theater charges $7 for adults, $5 for school-age children, and $3 for babies. A group of people went to the theater.
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 in the group?
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Let "x" be the number of school-age children.
Then the number of babies is "x" also, according to the condition,
and the number of adults is (x + x) = 2x, by the same reason.
The school-age children tickets cost 5x dollars.
The babies tickets cost 3x dollars.
The adult tickets cost 7*(2x) = 14x dollars.
Altogether, the tickets cost 5x + 3x + 14x = 22x dollars.
From the other side, this sum is 1562 dollars.
So you have this equation
22x = 1562,
which implies x = = 71.
Answer. 71 babies.
The lesson to learn from this solution:
1. First choose the major unknown reasonably.
2. Second, express other unknowns via the major unknown.
3. Then make an equation.
4. Then solve the equation.
It is the algorithm.
Again, this problem is about to teach you on how to select the unknown value by the rational and reasonable way.
It is not about writing the system of three equations in three unknowns.
It is not without reason they use the words "babies", "children" sending the message to you that the problem is
for very young students who only started study equations.
From this point of view, writing by "josgarithmetic" seems to be totally out of the goal of this assignment.