Download Homework 9

Homework 9
Provide a teacher’s solution to problem 1.
Problem 1
It takes Sisyphus two days to carry a pile of rocks up a hill. When I helped out,
it took us only 1.2 days to carry all of the rocks. How long would it take me to
carry the rocks by myself?
Problem 2
In the cafeteria where he works, John made 14 gallons of dessert containing
60% cream and 40% strawberries. His fellow worker Megan thought the dessert
looked too soupy, so she took out some cream from the mix. The remaining
dessert had 55% cream and 45% strawberries. How many gallons of cream did
she remove?
Problem 3
For each example, determine if the quantities are directly proportional, inversely
proportional, or neither.
a. The diameter and the circumference of a circle.
b. The length and width of a rectangle whose area is 10 square miles.
c. The amount of money I spend on beans and the number of bags of beans
I buy, given that one bag of beans costs $4.
d. The price of a bean and the number of beans I can buy with $100.
e. The number of hours I work and my take-home pay, given that I make
$18/hour and I pay a 30% tax rate.
f. The number of hours I work and my earnings after paying rent, given that
I make $18/hour and I pay $600 / month in rent.
g. The number of red M&Ms in a bag and the number of nonred M&Ms,
given that there are 100 M$Ms in the bag.
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Problem 4
Suppose A is directly proportional to B, B is inversely proportional to C and
C is inversely proportional to D. Determine whether A and D are directly
proportional, inversely proportional, or neither.
Problem 5
Recall our definitions of direct and inverse proportions.
a. One important equation from physics is F = ma, where F is the force of
a moving object, m is its mass, and a is its acceleration.
i. Choose one of these three variables so that, if it is held constant, the
remaining two quantities are in a directly proportional relationship.
Explain.
ii. Now choose one of the variables so that, if it is held constant, the
other two are in an inversely proportional relationship. Explain.
b. Another is the equation
m1 m2
r2
relating gravitational force F between two planets, where the distance
r between them, where m1 and m2 are the planets’ masses, and G is a
special constant (i.e., it’s not a variable).
F =G
i. Choose two of the four variables so that, if they’re held constant, the
remaining two quantities are in a directly proportional relationship.
Explain.
ii. Choose two of the quantities so that, if they’re held constant, the
other two are in an inversely proportional relationship. Explain.
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