Section P.9 Homework

1.  Balsamic vinegar contains 4% acetic acid, so a 8-oz bottle of balsamic vinegar contains____ ounces of acetic acid.

2. The formula d = rt  models the distance d traveled by an object moving at the constant rate r in time t. Find formulas for the following quantities.

r=

t=

3. Express the given quantity in terms of the indicated variable. The average of three test scores if the first two scores are 75 and 85;    s = third test score

4.  Express the given quantity in terms of the indicated variable.  The average of four quiz scores if each of the first three scores is 7;    q = fourth quiz score

5.  Express the given quantity in terms of the indicated variable.  The area (in ft²) of a rectangle that is three times as long as it is wide; w = width of the rectangle (in ft)

6.  Express the given quantity in terms of the indicated variable.  The value (in cents) of the change in a purse that contains twice as many nickels as pennies, two more dimes than nickels, and as many quarters as dimes and nickels combined;  p = number of pennies

7.  If Ben invests $5000 at 4% interest per year, how much additional money must he invest at

% annual interest to ensure that the interest he receives each year is 

% of the total amount invested?

8.  An executive in an engineering firm earns a monthly salary plus a Christmas bonus of $7500. If she earns a total of $89,100 per year, what is her monthly salary?

9.  A movie star, unwilling to give his age, posed the following riddle to a gossip columnist: “Six years ago, I was thirteen times as old as my daughter. Now I am seven times as old as she is.” How old is the movie star? ___ years old

10.  A pasture is twice as long as it is wide. Its area is 115,200 ft². How wide is the pasture?

11.  A man is walking away from a lamppost with a light source 4 m above the ground. The man is 2 m tall. How long is the man’s shadow when he is 10 m from the lamppost? [Hint: Use similar triangles.]  __m

12. A jeweler has four rings, each weighing 12 g, made of an alloy of 15% silver and 85% gold. She decides to melt down the rings and add enough silver to reduce the gold content to 80%. How much silver should she add? __g

13.  Two cyclists, 96 mi apart, start riding toward each other at the same time. One cycles twice as fast as the other. If they meet 4 h later, at what average speed is each cyclist traveling?

slower cyclist

faster cyclist

14. The figure shows a lever system, similar to a seesaw that you might find in a children’s playground. For the system to balance, the product of the weight and its distance from the fulcrum must be the same on each side; that is,w₁x₁ = w₂x₂.

This equation is called the law of the lever and was first discovered by Archimedes.

A woman and her son are playing on a seesaw. The boy is at one end, 7 ft from the fulcrum. If the son weighs 100 lb and the mother weighs 125 lb, where should the woman sit so that the seesaw is balanced?

15. This problem is taken from a Chinese mathematics textbook called Chui-chang suan-shu, or Nine Chapters on the Mathematical Art, which was written about 250 B.C.  A 6-ft-long stem of bamboo is broken in such a way that its tip touches the ground 3 ft from the base of the stem, as shown in the figure. What is the height of the break? [Hint: Use the Pythagorean Theorem.] ___ft

16. Find the length x in the figure if the shaded area is 128 cm².

17. A merchant blends tea that sells for $3.35 an ounce with tea that sells for $2.75 an ounce to produce 60 oz of a mixture that sells for $2.95 an ounce. How many ounces of each type of tea does the merchant use in the blend?

____ oz at $3.35/oz

____oz at $2.75/oz