MTH 030 -- Elementary Algebra -- Exercise Solutions
Section:

Elementary Algebra Exercises Section 2.5 Page 135

Solutions are shown in red

9) Use variables to write the formula relating the following:

a. Time, distance, rate d = rt

  1. Markup, retail price, cost r = c + m
  2. Costs, revenue, profit p = r c
  3. Interest rate, time, interest, principle I =prt
  4. Circumference, radius C = 2pr

 

14.    Tell which unit of measurement ft, ft2, ft3 would be appropriate when finding the following:

a.       The amount of storage space inside a safe. ft3

b.      The ground covered by a sleeping bag lying on the floor. ft2

c.       The distance the tip of an airplane propeller travels in one revolution. ft

d.      The size of the trunk of a car. ft3

22. 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 which we can

solve 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.

 

24. 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, costs 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 we 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.

26. 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) which 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.

 

30. 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.

 

32. 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 onece?

Solution: Use the formula C = 2pr which relates circumference and radius of a circle.

In this problem the radius is 28 and we will use 3.14 for p.

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.