Question

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 1

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