Difficulty: Hard

Average Score: 33%

A class has a budget of n dollars for a certain number n. The entire budget will be used to buy ribbons for a school event. In the following table, x represents the number of 50-cent ribbons and y represents the number of 1-dollar ribbons that can be bought using the entire budget.

Consider the following statement. “Joe's age, in years, is four more than three × Amy's age, in years.” If I represents Joe's age, in years, and A represents Amy's age, in years, which of the following equations represents the statement?

Rationale

J = 3A + 4

The statement "Joe's age, in years, is four more than three times Amy's age, in years" can be expressed mathematically by letting J represent Joe's age and A represent Amy's age. This formulation leads to the equation J = 3A + 4, indicating that Joe's age is derived from tripling Amy's age and then adding four.

A (A = J/3 + 4) YOUR ANSWER

This equation incorrectly implies that Amy's age is derived from Joe's age divided by three, plus four. However, the original statement indicates that Joe's age is based on Amy's age, not the other way around, making this choice inconsistent with the relationship described.

B (A = 3J + 4) YOUR ANSWER

This choice also misrepresents the relationship, suggesting that Amy's age is three times Joe's age plus four. The original statement explicitly states that Joe's age is dependent on Amy's, not the reverse, thus rendering this equation incorrect.

C (J = 3A + 4) CORRECT

This equation accurately reflects the relationship presented in the statement by showing that Joe's age (J) is equal to three times Amy's age (A) plus four years, correctly aligning with the description provided.

D (J = 3(A + 4)) YOUR ANSWER

This choice incorrectly suggests that Joe's age is three times the quantity of Amy's age plus four, which changes the meaning of the statement. The original relationship does not indicate that four should be added to Amy's age before multiplying by three.

Conclusion

The equation J = 3A + 4 correctly represents the relationship between Joe's age and Amy's age as stated in the question. The other options misinterpret the dependency between their ages, either by reversing the roles or incorrectly modifying the mathematical relationship. Thus, understanding the correct formulation is critical for accurately representing verbal statements in mathematical terms.

Consider the following statement. “Joe's age, in years, is four more than three × Amy's age, in years.” If I represents Joe's age, in years, and A represents Amy's age, in years, which of the following equations represents the statement?

J = 3A + 4

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test