Question

In the following formula, y is the minimum number of hours of studying required to attain a test score of x: y= 0.34x/100.5-xHow many hours of study are needed to score 90? Round your answer to the nearest hundredth, if necessary.

Answer 1

In this problem, we are given a function that represents how much time is needed to attain a desired score:

`y=(0.34x)/(100.5-x),`

where y represents the minimum number of hours, and x represents the desired test score.

Luckily, we can use direct substitution in this problem, which means we add the desired test score and simplify.

We want a score of 90, which means

`x=90`

Substituting that into our equation, we get:

`y=(0.34(90))/(100.5-(90))`

Simplify the numerator and denominator:

`y=(30.6)/(10.5)`

Divide:

`y\approx2.91`

It will take approximately 2.91 hours to get a score of 90 on the test.