on his first exam, he studied for 10 hours and went to tell the mall for 4hours, and got a score of 85. how long should he study to get a grade of 96 and go to the mall for 17 hours?
grade varies directly with studying and inversely with going to the mall.
is the answer 48hrs?
Mark = k(s)/m, where s is number of hrs studying, m is the number of hrs at the mall, and k is a constant
given: Mark = 85, s=10, m=4
85 = k(10)/4
k = 34
Mark = 34s/m
96 = 34s/17
s = 48 hrs
(a rather silly question)
To find out how long he should study to get a grade of 96 and go to the mall for 17 hours, we can use the concept of direct and inverse variation.
Let's assign variables:
- Let "x" represent the number of hours he needs to study.
- Let "y" represent the number of hours he goes to the mall.
According to the given information, we have the following proportions:
Studying: 10 hours --> Grade: 85
Studying: x hours --> Grade: 96
Therefore, we can write the direct variation equation for studying:
10/x = 85/96
Simplifying the equation:
10/x = 17/20
Cross-multiplying:
17x = 200
Solving for x:
x = 200/17
x ≈ 11.76 hours
So, he needs to study approximately 11.76 hours to get a grade of 96.
Now, let's check the inverse variation for going to the mall:
Going to the mall: 4 hours --> Grade: 85
Going to the mall: y hours --> Grade: 96
In this case, since the grade varies inversely, the equation is:
4y = 85 * 96
Simplifying:
4y = 8160
Solving for y:
y = 8160/4
y = 2040 hours
So, he would need to go to the mall for approximately 2040 hours to get a grade of 96.
Therefore, the answer is not 48 hours. The correct answer is approximately 11.76 hours of studying and approximately 2040 hours of going to the mall. Please note that going to the mall for such a long duration may not be practical or realistic.