Question 182997
Let's start by seeing what the student earned in the first half of the course.
He/she earned 81% of 120 points. That's 0.81(120) = 97.2 points.
So we let x = the percentage that the student must earn in the second half of the course so that the the final grade is 80% of 260 (120+140) points., so...
Take the total points earned (97.2+x(140)) and divide by the total points available (260) and this is to equal 80% (0.8).
{{{(97.2+140x)/260 = 0.8}}} Multiply both sides by 260.
{{{97.2+140x = 0.8(260)}}}
{{{97.2+140x = 208}}} Subtract 97.2 from both sides.
{{{140x = 110.8}}} Divide both sides by 140.
{{{x = 0.791429}}} or x = 79.1429%
The number of points the student needs in the second half is 79.01429% of 140.
{{{highlight(0.791429(140) = 110.8)}}}points.
Check:
The number of points earned in the first half (97.2) plus the number of points earned in the second half (110.8) all divided by the total points available (260) should equal 0.8 or 80%.
{{{(97.2+110.8)/260 = 0.8}}} or 80% OK!