1)  Problem:  Rose Parade floats travel down the 5.5 mile-long parade route at a rate of 2.5 mph. How long will it take a float to complete the parade if there are no delays?
Solution: Use the formula d = rt which relates distance, rate and time.
In this case we know the distance is 5.5 and we know the rate is 2.5.
So we have 5.5 = (2.5)t  
we can solve this equation for t by dividing both sides of the equation by 2.5 to obtain:
     
It will take a float 2.2 hours to traverse the parade route.
Note that .2 of an hour is (.2)60 =12 min.
It will take a float 2 hrs. 12 min. to traverse the parade route.

2)  Problem:  After expenses of $55.15 were paid, a Rotary Club donated $875.85 in proceeds from a pancake breakfast to a local health clinic. How much did the pancake breakfast gross?
Solution: Use the formula p = r – c which relates profit, cost and revenue.
In this problem the profit is $875.85 and the cost is $55.15.
So we have 875.85 = r – 55.15 which w
W e can solve for r by adding 55.15 to both sides of the equation to obtain:
      r = 875.85 + 55.15 = $931
The Rotary Club had a gross of $931 from their pancake breakfast.

3)  Problem: The factory invoice for a minivan shows that the dealer paid $16,264.55 for the vehicle. If the sticker price of the van is $18,202, how much over factory invoice is the sticker price.
Solution: Use the formula r = c + m which relates cost, markup and retail price.
In this problem the cost is $16,264.55 and retail price is $18,202.
This gives the equation 18202 = 16264.55 + m which
We can solve for m by subtracting 16264.55 from both sides of the equation to obtain:
     m = 18202 – 16264.55 = 1937.45
The sticker price is $1937.45 over factory invoice.

4)  Problem:   A horse trots in a perfect circle around its trainer at the end of a 28-foot-long rope. How far does the horse travel as it circles the trainer once?
Solution: Use the formula C = 2πr which relates circumference and radius of a circle.
In this problem the radius is 28 and we will use 3.14 for π.
This give the equation C = (2)(3.14)(28) = 175.84
Therefore the horse travels 175.84 feet or approximately 176 feet each time it circles the trainer.

5)  Problem:   Three years after opening an account that paid 6.45% annually, a depositor withdrew the $3,483 in interest earned. How much money was left in the account?
Solution: Use the formula I = prt which relates principle, rate, time, and interest.
In this problem the interest is 3483, rate is 6.45% = .0645, and time is 3
This gives the equation 3483 = p(.0645)(3)
We can solve for p by dividing both sides of the equation by (.0645)(3) to obtain:
     
There was $18,000 left in the account.
This was the amount originally deposited.

6)  Problem:   Omaha, Nebraska is about 90 miles from, Lincoln, Nebraska. Susan must go to the law library in Lincoln to get a dcoument for the law firm she works for in Omaha.How long will it take her to drive round-trip if she averages 50 miles per hour.
Solution:  Use the formula d = rt which relates distance, rate and time.
In this problems the distance is 180 miles and rate is 50 mph.
This gives the equation 180 = (50)t.
We can solve this equation for t by dividing both sides of the equation by 50 to obtain:
     
It will take her 3.6 hours to drive the round trip.
Observe that 0.6 hours is (.6)(60) = 36 minutes.
Therefore it will take her 3 hours and 36 minutes to drive the round trip.

7)  Problem:   It took Jake 5.5 hours to drive 154 miles. What was his average speed?
Solution:  Use the formula d = rt which relates distance, rate and time.
In this problem distance is 154 mile, time is 5.5 hours and rate is what we wish to compute.
This gives the equation 154 = (5.5)r
Solve this equation by dividing both sides of the equation by 5.5 to obtain:
     
Jake's average speed was 28 mph.

8)  Problem:   One-foot-square ceiling tiles are sold in packages of 50. How many packages must be bought for a rectangular ceiling 18 feet by 12 feet.
Solution:  Use the formula for the area of a rectangle Area = (length)(width) to determine the area of the ceiling is (18)(12) = 216 sq.ft.
Each package of tiles will cover 50 square feet. Therefore this ceiling will require packages.
Partial packages are not sold. Therefore 5 packages of tiles are required.

9)  Problem:   A gallon of latex paint can cover 500 square feet. How many gallon containers of paint should be bought to paint two coats on each wall of a rectangular room which is 16 feet long, 14 feet wide, and 8 feet high.
Solution:  Begin by computing the area of the walls.
There are two rectangular walls which are 8 ft. by 16 ft.
These two have an area of (2)(8)(16) = 256 sq.ft.
There are two rectangular walls which are 8 ft. by 14 ft.
These two have an area of (2)(8)(14) = 224 sq. ft.
The four walls have a total area of 256 + 224 = 480 sq.ft.
Painting them twice means painting (2)(480) = 960 sq.ft.
Each gallon of paint covers 500 sq. ft. so gallons of paint are required.
Therefore 2 gallons must be purchased.

10)  Problem:   A serving of cashews contains 14 grams of fat, 7 grams of carbohydrate, and 6 grams of protein. How many calories are in a serving of cashews?
Solution:  Use the formula C = 4h + 9f + 4p which relates calories, carbohydrates, fat, and protein.
In this problem, h = 7, f = 14, and p = 6.
This yields C = 4(7) + 9(14) + 4(6) = 178
A serving of cashews contains 178 calories.

11)  Problem:   A serving of chocolate contains 9 grams of fat, 30 grams of carbohydrates, and 2 grams of protein. How many calories are in a serving of chocolate?
Solution:   Use the formula C = 4h + 9f + 4p which relates calories, carbohydrates, fat, and protein.
In this problem, h = 30, f = 9 and p = 2.
This yields C = 4(30) + 9(9) + 4(2) = 209.
A serving of chocolate contains 209 calories.

12)  Problem:   A serving of raisins contains 130 calories and 31 grams of carbohydrates. If raisins are fat-free, how much protein is provided by a serving of raisins?
Solution:  Use the formula C = 4h + 9f + 4p which relates calories, carbohydrates, fat, and protein.
In this problem, C = 130, h = 31, f = 0.

This yields 130 = 4(31) + 9(0) + 4p = 124 +4p
Solve this equation for p by subtracting 124 from both sides of the equation to obtain
     6 = 4p
Now divide both sides of the equation by 4 to obtain
     p = 1.5
There are 1.5 grams of protein in a serving of raisins.

13)  Problem:   How much interest is earned by $10,000 in 2 years in a certificate of deposit which pays 8,5% interest compounded quarterly?
Solution: Use the formula for compound interest
In this problem we know P = 10,000, r = 8.5% = 0.085, n = 4, and t = 2.
This yields    = 11831.96
Because the original deposit was $10,000, the interest is $11831.96 - $10000 = $1831.96