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.
Answer (2)
Jeff's age is 3 years less than Tony's age: J = T − 3 .
The total cost of Marie's balloons is $3 t im es t h e n u mb ero f ba ll oo n s : M = 3b$.
The skate rental cost includes an additional $3 : S = 3 + rh$, where r is the hourly rental rate and h is the number of hours.
The equations model the relationships described in each scenario. $\boxed{\text{See equations in summary}}.
Explanation
Analyzing the Scenarios Let's analyze each scenario and match it with the correct equation.
Scenario 1: Jeff's age Scenario 1: Jeff is 3 years less than Tony's age. Let J be Jeff's age and T be Tony's age. The equation that represents this scenario is: J = T − 3
Scenario 2: Cost of Balloons Scenario 2: Marie buys balloons for a party that are $3.00 e a c h . L e tM b e t h e t o t a l cos t o f t h e ba ll oo n s an d bb e t h e n u mb ero f ba ll oo n s . T h ee q u a t i o n t ha t re p rese n t s t hi ssce na r i o i s : M = 3 b $
Scenario 3: Skate Rental Cost Scenario 3: Skate rental charges an additional $3. L e tS b e t h e t o t a l cos t o f t h es ka t ere n t a l . T hi ssce na r i o im pl i es t ha tt h ere i s a f i x e d c ha r g eo f $3 plus some other cost, which could be hourly rental fees. If we let h be the number of hours and r be the rental cost per hour, the equation is: S = 3 + r h However, without knowing the hourly rate, we can only say that the total cost S is $$3 plus some other cost.
Summary of Equations In summary:
Jeff is 3 years less than Tony's age: J = T − 3
Marie buys balloons for a party that are $3.00 e a c h : M = 3b$
Skate rental charges an additional $3 : S = 3 + rh ( or S = 3 + \text{other costs}$ if the hourly rate is unknown)
Examples
Understanding how to translate word problems into mathematical equations is a fundamental skill that applies to many real-life situations. For example, if you're planning a party and need to calculate the total cost of pizza, where each pizza costs $15 an d t h er e ′ s a d e l i v ery f eeo f $5, you can model this with the equation C = 15 p + 5 , where C is the total cost and p is the number of pizzas. Similarly, if you're tracking your savings and you save $50 p er m o n t h , b u t s t a r t e d w i t hanini t ia l d e b t o f $200, the equation S = 50 m − 200 models your savings S after m months. These simple equations help in budgeting, financial planning, and making informed decisions.
In the given scenarios, the equations that model each situation are: Jeff's age can be represented as J = T − 3 , the cost of balloons is represented as M = 3 b , and the total cost for skate rental can be expressed as S = 3 + r h . This breakdown translates the scenarios into mathematical relationships effectively.
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