Bethany is 15 years older than twice Mary's age.
$B=2 M+15$
Answer (2)
Define variables B and M for Bethany's and Mary's ages.
Translate 'twice Mary's age' into 2 M .
Express '15 years older than twice Mary's age' as 2 M + 15 .
Formulate the equation B = 2 M + 15 and identify it as the correct option. B = 2 M + 15
Explanation
Understanding the Problem We are given the statement 'Bethany is 15 years older than twice Mary's age' and four equations relating Bethany's age (B) and Mary's age (M). Our goal is to determine which of the four given equations correctly represents the statement.
Defining Variables Let B represent Bethany's age and M represent Mary's age. We need to translate the given statement into an algebraic equation.
Expressing Twice Mary's Age Twice Mary's age is represented as 2 M .
Expressing '15 years older than twice Mary's age' '15 years older than twice Mary's age' is represented as 2 M + 15 .
Formulating the Equation Therefore, Bethany's age (B) is equal to 2 M + 15 , which gives the equation B = 2 M + 15 .
Comparing with Given Equations Now, we compare this equation with the four given equations:
B = 2 M − 15
M = 2 B + 15
2 B = M + 15
B = 2 M + 15
We can see that equation 4, B = 2 M + 15 , matches the equation we derived from the given statement.
Final Answer Therefore, the correct equation is B = 2 M + 15 .
Examples
Understanding how to translate word problems into algebraic equations is a fundamental skill in mathematics. For example, if you are trying to determine the cost of a service that charges a fixed fee plus an hourly rate, you can use a similar approach. If a plumber charges a fixed fee of $50 plus 75 p er h o u r , t h e t o t a l cos t ( C ) f or hh o u rso f w or k c anb ere p rese n t e d a s C = 75h + 50$. This is a linear equation that helps you calculate the total cost for any number of hours the plumber works.
Bethany's age can be represented by the equation B = 2 M + 15 , where M is Mary's age. This equation shows that Bethany is 15 years older than twice Mary's age. Therefore, the correct formulation is established as stated.
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