030 -- Elementary Algebra -- Exercise Solutions
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
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?
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.