Use the information to find a linear algebraic equation...

Use the information to find a linear algebraic equation model to use to answer the question being asked.Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has I more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is $113 ?$

Key Concepts

Variable Assignment

This concept involves assigning variables to represent unknown quantities in a problem. By letting a variable, such as x, stand for one of the unknowns (for example, the number of marbles Mark has), it becomes possible to express related quantities in terms of that variable, thereby creating a basis for forming algebraic equations.

Translating Word Problems into Algebraic Equations

This involves interpreting the language of the problem and converting verbal descriptions into mathematical expressions. For instance, a phrase like 'Don has 1 more than 3 times the number of marbles Mark has' can be translated into an algebraic expression such as 3x + 1, which then forms part of the equation model.

Forming a Total Sum Equation

When a problem mentions a total sum for the quantities involved, it is crucial to set up an equation that sums the individual expressions representing each part to this total. In this context, this would involve adding the expression for Mark's marbles and the expression for Don's marbles to equate to the given total, resulting in a linear equation.

Solving Linear Equations

Once a linear equation is established, the next step is to use algebraic methods like combining like terms and isolating the variable to solve for the unknown quantity. This process transforms a verbal description into a quantifiable solution using the fundamentals of linear algebra.

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