Solve multi-step algebraic word problems

This understanding involves translating a multi-step situation into an algebraic expression or one-variable equation, identifying what the variable represents, and preserving the relationships among known and unknown quantities. The learner evaluates expressions using the order of operations and solves simple linear equations with whole numbers, fractions, or decimals by applying inverse operations, then checks that the solution fits the context and units. Systems of equations, quadratic equations, inequalities, and more abstract symbolic generalizations are not included.

Detailed Explanation: Solve multi-step algebraic word problems

To solve a multi-step algebraic word problem:

Choose a variable for the unknown amount.
Translate the words into an equation.
Solve the equation using inverse operations.
Check that the answer makes sense in the situation.

Example

At a school fair, admission costs $5. Each game costs $3. Lena spends $26 total. How many games does she play?

1. Choose a variable

Let $g$ represent the number of games Lena plays.

2. Write an equation

The total cost is the admission fee plus the game costs:

5+3g=26

Here, $3g$ means $3 for each of $g$ games.

3. Solve the equation

First, subtract $5$ from both sides:

5+3g-5=26-5

3g=21

Then divide both sides by $3$ :

\frac{3g}{3}=\frac{21}{3}

g=7

4. Check the answer

If Lena plays $7$ games, the total cost is

5+3(7)=5+21=26

The total is $26, so the answer is correct.

Lena plays $\boxed{7}$ games.

Learn by doing: Solve multi-step algebraic word problems

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Algebra Meals - 2 Meals, 1 Item, to Answer

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