Bob believes his test grade varies directly with the number of hours he spends studying and inversely with the number of hours he spends playing baseball. On his first test, he spent 6 hours studying and 7 hours playing baseball and scored a 72. What score should he expect on his second test if he studies 4 hours and plays baseball for 6 hours? What score should Bob expect on his second test? nothing

Answer: Hello mate!

A direct variation implies that, if y is the dependent variable that varies with the variable x; then: y = k*x where k is a real number.

An inverse variation has the form y = k/x where also k is a real number.

them, if we define s as the hours that Bob spends studying, and b as the hours that he spends playing baseball, then the equation that represents the score is:

Score (s, b) = k*s/b

we know that if s = 6, and b = 7, then the score is 72; with this information, we could obtain the value of the constant k.

score (6,7) = 72 = k*6/7 = k*

then k = 72 * (7/6) = 61.7

now if s = 4 and b = 6, the score that he should expect is:

score (4, 6) = 61.7 * (4/6) = 41