Q: According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24. Over your lifetime, how many years will you spend on each of these activities?

$$\text{Sleeping: } 28 \text{ years, Eating: } 4 \text{ years}$$

Question 1

According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24. Over your lifetime, how many years will you spend on each of these activities?

Accepted Answer

$$	ext{Sleeping: } 28 	ext{ years, Eating: } 4 	ext{ years}$$

Question 2

A discount pass for a bridge costs $$30 per month. The toll for the bridge is normally 5.00$$, but it is reduced to $3.50 for people who have purchased the discount pass. Determine the number of times in a month the bridge must be crossed so that the total monthly cost without the discount pass is the same as the total monthly cost with the discount pass.

Accepted Answer

$$20$$

Question 3

You are choosing between two texting plans. Plan A has a monthly fee of $$15 with a charge of 0.08 $$per text. Plan B has a monthly fee of $$3 with a charge of 0.12 $$per text. For how many text messages will the costs for the two plans be the same?

Accepted Answer

$$300$$

Question 4

After a $$30\%$$ price reduction, you purchase a new computer for $840. What was the computer’s price before the reduction?

Accepted Answer

$$1200$$

Question 5

You inherited $$5000 with the stipulation that for the first year the money had to be invested in two funds paying 9$$\%$$ and 11$$\%$$ annual interest. How much did you invest at each rate if the total interest earned for the year was 487$$?

Accepted Answer

$$3150 at$$ $$9\%$$, $$1850 at$$ $$11\%$$

Question 6

The length of a rectangular basketball court is $$44$$ feet more than the width. If the perimeter of the basketball court is $$288$$ feet, what are its dimensions?

Accepted Answer

$$50 ft by$$ $$94 ft$$

Question 7

Solve the formula for the area of a triangle, $$A = \frac{1}{2}bh$$, for $$h.$$

Accepted Answer

$$h = \frac{2A}{b}$$

Question 8

A rectangular garden has a length that is twice its width. If the perimeter is $$60$$ meters, what are the dimensions of the garden?

Accepted Answer

$$10 m by$$ $$20 m$$

Question 9

If the circumference of a circle is $$C = 2\pi r$$, solve for $$r in $$terms of $$C.$$

Accepted Answer

$$r = \frac{C}{2\pi}$$

Question 10

A cube has a volume of $$V = s^3$. If the volume is 64$ cubic units, what is the length of one side?

Accepted Answer

$$4$$ units

Question 11

A cone has a volume of $$V = \frac{1}{3}\pi r^2$ h. If $$the volume is $$150\pi$$ cubic centimeters and the height is $$10 cm$$, what is the radius?

Accepted Answer

$$r = 5 cm$$

Question 12

A rectangular solid has a volume of $$V = lwh. If $$the length is $$8 cm$$, the width is $$5 cm$$, and the height is $$3 cm$$, what is the volume?

Accepted Answer

$$120$$ 	ext{ cm}^3$

Question 13

If the area of a trapezoid is $$A = \frac{1}{2}(b_1$ + b_2$)h$$, solve for $$h in $$terms of $$A$$, $$b_1$$, and $$b_2.$$

Accepted Answer

$$h = \frac{2A}{b_1$ + b_2$}$$

Question 14

A circular cylinder has a volume of $$V = \pi r^2$ h. If $$the volume is $$100\pi$$ cubic inches and the height is $$4$$ inches, what is the radius?

Accepted Answer

$$r = 5$$ 	ext{ inches}$

Solving Linear Equations and Applications in College Algebra

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