Maths Ten Misc. problems

1. Race track A has 32,000 more grandstand seats than three times the number of grandstand
seats at another race track B. Together, these two race tracks seat 280,000 auto racing fans.
How many seats does each race track have?

2. The average annual number of cigarettes smoked by an adult in some countries continues to
decline. For the years 1997-2006, the equation y = -49.6x + 1756.7 approximates this data.
Here x, is the number of years after 1997 and y is the average annual number of cigarettes
smoked. If this trend continues, find the year in which the average number of cigarettes smoked
is zero. To do this, let y = 0 and
solve for x.

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3. A gallon of latex paint can cover 2000 square feet. Maria has a rectangular room whose
dimensions are 17 feet by 16 feet, with 10-foot ceilings. How many gallon containers of paint
does she need to buy to paint two coats on each wall?

4. Scientists are drilling a hole in the ocean floor to learn more about the Earth’s history.
Currently, the hole is in the shape of a cylinder whose volume is approximately 3500 cubic feet
and whose height is 4.2 miles. Find the radius of the hole to the nearest hundredth of a foot.
(Hint: Make sure the same units of measurement are used.)

5. The distances between objects in space are so great that other units other than miles or
kilometers are often used. For example, the astronomical unit (AU) is the average distance
between Earth and the sun, or 92,900,000 miles. Use this information to convert the distance of
some planets in miles from its star to astronomical units. The planet is 532.1 million miles from
the star.

6. The average consumption per person per year of whole milk can be approximated by the
equation w = -1.9t + 70.1 where t is the number of years after 1996 and w is measured in pounds. The consumption of whole milk is shown on the graph in blue. Determine when the consumption of
whole milk will be less than 40 pounds per person per year.

7. List the integers that make both inequalities true.
x ≥ -7 and x ≥ 8

8. Solve the compound inequality.
2x ≥ 7 or – x – 9 > 3

9. Solve the compound inequality.
0< <7

10. Solve the compound inequality for x. Write the solution set in interval notation.
2x – 4 < 3x + 2 < 4x – 7

11. Solve the compound inequality for x. Write the solution set in interval notation.
7x – 4 < 2(3 + x) < -2 (12 + 2x)