Question

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?

y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.
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.
y=20x+2; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.
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.

Answer 1

let's look at the time he spent doing math problems

it says he did (x) math problems, at 2 minutes each. therefore, you would multiply 2*x to get the time he spent doing math.

add this on to the 20 minutes he spent doing history. ---> 2x + 20 which narrows us down to choices 1 and 2

now, to distinguish between choices 1 and 2, it's asking whether the domain and range are integers or just real numbers in general. remember that integers are positive and negative whole numbers (-1,0,1, 2, etc.) while real numbers are just non-imaginary numbers (a.k.a no "i" values)

so, thinking about what the domain and range represent in real life (x = number of homework problems and y = time spent doing hw) can these values be non-integers?