Question 18 • GA-Algebra: Concepts and Connections CR
Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. What is the equation that can be used to find the value of y, the total time that Vlad spent on his homework, and what are the constraints on the values of x and y?
Answer
A
y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.
B
y=2x+20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.
C
y=20x+2; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.
D
y=20x +2; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.
Explanation
Vlad spends 20 minutes on history and 2 minutes for each of x math problems, so the total time is y = 20 + 2x. Since x counts completely solved problems, it must be a whole number at least 0. Thus y is also an integer and cannot be less than 20 minutes, matching “y = 2x + 20” with the stated constraints.
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