As the treasurer of her daughter's Girl Scout troop, Laney...

As the treasurer of her daughter's Girl Scout troop, Laney collected money for some girls and adults to go to a 3day camp. Each girl paid $$\$ 75$$ and each adult paid $$\$ 30.$$ The total amount of money collected for camp was $$\$ 765 .$$ If the number of girls is three times the number of adults, how many girls and how many adults paid for camp?

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Key Concepts

Proportional Relationships

Proportional relationships occur when one quantity is a fixed multiple of another. Recognizing these relationships is crucial in word problems where, for example, one group is specified to be a certain multiple of another, as it directly informs the way the equations are set up and solved.

Substitution Method

The substitution method is an algebraic technique used to solve systems of equations. It involves solving one equation for one variable and then substituting that expression into the other equations, thereby reducing the number of variables and simplifying the system to a single equation.

System of Linear Equations

A system of linear equations involves setting up two or more equations that relate multiple variables. In solving word problems, these equations model relationships between different quantities, such as costs and counts, allowing the unknown values to be determined simultaneously.

Variable Assignment

Variable assignment is the process of designating symbols to represent unknown quantities in a problem. This is essential in transforming a word problem into mathematical equations that can be manipulated and solved to find the desired values.

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