math for liberal arts

Question

#1). The population of a town increased from 3250 in 2008 to 4950 in 2010. Find the absolute and relative (percent) increase.

Absolute increase: 

Relative increase:%

Give answers accurate to at least 1 decimal place.

#2) A store has clearance items that have been marked down by 40%. They are having a sale, advertising an additional 25% off clearance items. What percent of the original price do you end up paying?

%

Give your answer accurate to at least one decimal place.

#3)A friend has a 83% average before the final exam for a course. That score includes everything but the final, which counts for 30% of the course grade.

What is the best course grade your friend can earn?  %

What is the minimum score would your friend would need on the final to earn a 75% for the course? %

Give answers accurate to at least one decimal place.

#4)A car is driving at 45 kilometers per hour. How far, in meters, does it travel in 2 seconds?

 meters

Give your answer to the nearest meter.

Answer 1

1) 4950-3250 = 1600 = absolute increase

1600/3250 = 160/325 = 32/65 = about 49.23% percentage increase per 2 years

or

49.23/2 = about 24.62% annual percentage increase

2) 40% then another 25% discount. final price is what % off?

100 with 40% off is 60

60 with 25% off is .75(60) = 45 final price

which is 55% off the original price

55% off is the total discount (not 40+25=65 which you might be tempted to try)

3) 83 counts 70% final exam 30%

final grade will be .7(83) +.3x = .3x + 58.1

if 100 is the maximum final exam grade possible (no extra credit questions)

then

maximum possible final grade = 58.1 +.3(100) = 58.1+30 = 88.1

88.1

to get a final grade of 75

.3x + 58.1 = 75

.3x = 75-58.1 = 16.9

x = 16.9/.3 = 56.3 is needed on the exam to get a 75 final grade

4) 45 kph = how many meters per second?

45 kph = 45(1000)/2(60)(60) m/sec since 1km = 1000 m, 1 hr = 3600 seconds

= 45000/7200 = 450/72 =225/36 = 6 1/4 meters per second