Which word problem has a solution of |-40| = |40|? ?

A. Mike gained 40 pounds but then lost 15 pounds. How many pounds did Mike gain?
B. Alice was paid $300. The next day her boss realized he made a mistake and gave her another $40. What is the magnitude of Alice's salary adjustment?
C. Amy paid Dan back $40. How much money did Dan receive?
D. Joe meets up with a friend and spends $40 for a meal. How much did Joe spend for a meal?

1 answer

To determine which word problem has a solution of |-40| = |40|, we need to analyze the absolute values in the context of each problem.

  • |-40| represents the absolute value of -40, which is 40.
  • |40| represents the absolute value of 40, which is also 40.

Both absolute values are equal, so we are looking for a word problem that reflects a situation involving positive and negative values, where we care about the magnitude of an adjustment or amount.

Let’s analyze the options:

A. Mike gained 40 pounds but then lost 15 pounds. How many pounds did Mike gain?

  • The total change in weight would require calculations, but it does not directly reflect |-40| and |40| since it focuses on gaining and losing pounds, not an absolute amount.

B. Alice was paid $300. The next day her boss realized he made a mistake and gave her another $40. What is the magnitude of Alice's salary adjustment?

  • The adjustment involves an additional $40, which is positive. The total adjustment from the $300, considering the mistake, is not explicitly about negative and positive amounts equal to |-40| and |40|.

C. Amy paid Dan back $40. How much money did Dan receive?

  • This reflects a payment of $40, which is positive, but again does not represent a context involving |-40|.

D. Joe meets up with a friend and spends $40 for a meal. How much did Joe spend for a meal?

  • Joe spent $40, which means his actual spending is treated as a positive $40. The situation doesn't indicate any negative value.

Upon reviewing all options, none quite fits the expression |-40| = |40| directly. However, option C, while simply stating Dan received $40, works with the idea of owing back money (a negative context turning into a positive when discussing absolute value).

Most closely related to the concept of absolute values (even if slightly off) is Option C: Amy paid Dan back $40. How much money did Dan receive? The focus on magnitude could imply the positive resolution tied to the relationship of the contexts involving debts or payments.

However, it’s essential to note that if we're strictly adhering to interpreting the problem as needing the mathematical expression to be resolved clearly to equal the absolute values mentioned, none seem to embody the expression perfectly. Option B is closely aligned because it refers to an adjustment amount, but only option C directly talks about a monetary return, making it the best fit given absolute consideration from a financial perspective.