Example Card: Application Problem
Solve application word problems using algebraic equations in Grade 9 Algebra. Translate the scenario into an equation, solve, and interpret the answer in context.
Key Concepts
Let's see how substitution solves real world puzzles involving money and quantities, like figuring out sales at a bake sale.
Example Problem At a bake sale, large cookies cost 3 dollars and small cookies cost 2 dollars. In total, 40 cookies were sold, and the total revenue was 95 dollars. How many large and small cookies were sold?
Step by Step 1. First, define the variables for our unknowns. Let $L$ = number of large cookies sold. Let $S$ = number of small cookies sold. 2. Translate the situation into a system of two equations. Equation for the total number of cookies: $$L + S = 40$$ Equation for the total revenue: $$3L + 2S = 95$$ 3. Use substitution to solve. First, solve the simplest equation, $L + S = 40$, for one variable. Let's solve for $S$: $$S = 40 L$$ 4. Substitute this expression for $S$ into the second equation: $$3L + 2(40 L) = 95$$ 5. Distribute the $2$: $$3L + 80 2L = 95$$ 6. Combine the like terms ($3L$ and $ 2L$): $$L + 80 = 95$$ 7. Subtract $80$ from both sides to find $L$: $$L = 15$$ 8. Substitute $L = 15$ back into the equation $S = 40 L$ to find $S$: $$S = 40 15$$ $$S = 25$$ 9. The solution is $(15, 25)$. This means 15 large cookies and 25 small cookies were sold.
Common Questions
What is Example Card: Application Problem in Grade 9 Algebra?
Let's see how substitution solves real-world puzzles involving money and quantities, like figuring out sales at a bake sale Mastering this concept builds a foundation for advanced algebra topics.
How do you approach Example Card: Application Problem problems step by step?
Example Problem At a bake sale, large cookies cost 3 dollars and small cookies cost 2 dollars Use this method consistently to avoid common errors.
What is a common mistake when studying Example Card: Application Problem?
In total, 40 cookies were sold, and the total revenue was 95 dollars Always check your work by substituting back into the original problem.