Lisa studies 8 hrs. for a particular test and gets a score of 78. at this rate how many hours would she have to study to get a score of 98?
There is no reason to assume that the hours spent studying are proportional to the score. If there were, a score of over 100 would be possible.
Lisa studies 8 hrs. for a particular test and gets a score of 78. at this rate how many hours would she have to study to get a score of 98?
To determine the answer, we need to find the relationship between the number of hours Lisa studies and her test score. We can start by representing this relationship as a linear equation.
Let's assume that the number of hours Lisa studies is represented by "x," and her test score is represented by "y." Based on the information given, we know that Lisa studies for 8 hours and gets a score of 78. So, we have the coordinates (8, 78).
We can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, "m" represents the slope and "b" represents the y-intercept. By substituting the values we know into this equation, we can solve for the unknowns.
We have:
78 = 8m + b
To find the slope, we need another point on the line. Since we only have one point, we can't calculate the slope directly. However, we can assume that the relationship between study time and score is consistent and use the given information to find the slope.
Let's assume that Lisa needs to study "h" hours to get a score of 98. So we have the coordinates (h, 98).
Using the formula for slope (m = (y2 - y1) / (x2 - x1)), we can find the slope of the line.
m = (98 - 78) / (h - 8)
Now, we can substitute the value of the slope into the equation we generated earlier (78 = 8m + b) to solve for the y-intercept (b).
78 = 8((98 - 78) / (h - 8)) + b
Next, we can substitute the value of the slope (m) and solve for the y-intercept (b).
78 = (8 * 20) / (h - 8) + b
Simplifying, we have:
78 = 160 / (h - 8) + b
To find the value of b, we can solve for it.
b = 78 - 160 / (h - 8)
Now, we have both the slope (m) and y-intercept (b) of the linear equation, which is y = mx + b. We can rewrite the equation using the values we found:
y = (160 / (h - 8)) * x + (78 - 160 / (h - 8))
We want to find the study time (x) when the score (y) is equal to 98. So, we can substitute the values into the equation:
98 = (160 / (h - 8)) * x + (78 - 160 / (h - 8))
Now, we can solve this equation for x, which represents the number of hours Lisa needs to study to get a score of 98.