**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**

- Markup, retail price, cost
**r = c + m** - Costs,
revenue, profit
**p = r – c** - Interest
rate, time, interest, principle
**I =prt** - Circumference,
radius
**C = 2****p****r**

14.
Tell which unit of measurement – ft, ft^{2}, ft^{3}
– would be appropriate when finding the following:

a.
The amount of storage space inside a safe. **ft ^{3}**

b.
The ground covered by a sleeping bag lying on the floor. **ft ^{2}**

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

d.
The size of the trunk of a car. **ft ^{3}**

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?

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 = 2****p****r** 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.