Match up each scenario with the equation that models the word problem: Jeff is 3 years less than Tony's age. Marie buys balloons for a party that are $3.00 each. Skate rental charg... Match up each scenario with the equation that models the word problem: Jeff is 3 years less than Tony's age. Marie buys balloons for a party that are $3.00 each. Skate rental charges an additional $3.
Understand the Problem
The question requires matching word problem scenarios with their corresponding equations. Each scenario describes a situation involving relationships between ages and costs, and the task is to determine the correct mathematical representation for each description.
Answer
- Jeff's age: $y = x - 3$ - Marie's balloons: $y = 3x$ - Skate rental: $y = x + 3$
Answer for screen readers
- Jeff's age: $y = x - 3$
- Marie's balloons: $y = 3x$
- Skate rental: $y = x + 3$
Steps to Solve
-
Understanding Jeff's Age Relationship
Jeff's age is described as being 3 years less than Tony's age. This can be represented as:
Let $x$ represent Tony's age. Therefore, Jeff's age is $y = x - 3$. -
Understanding Marie's Balloon Purchase
Marie buys balloons for $3.00 each. If we let $x$ represent the number of balloons she buys, then the total cost can be expressed as:
$y = 3x$ (where $y$ is the total cost). -
Understanding Skate Rental Charges
The scenario mentions that skate rental charges an additional $3. We can express this if we let $x$ be the base rental fee, thus the total charge becomes:
$y = x + 3$.
- Jeff's age: $y = x - 3$
- Marie's balloons: $y = 3x$
- Skate rental: $y = x + 3$
More Information
This matching process illustrates how word problems can be translated into mathematical equations, focusing on relationships between variables. Understanding how to identify these relationships is essential for solving similar problems in the future.
Tips
- Confusing the relationships: Ensure to identify correctly whether the relationship is an addition or subtraction scenario.
- Misinterpreting the cost structure: When problems involve costs, clarify if it’s a total cost or a per-item cost.
