Question

1. The number of calculators Mrs. Hopkins can buy for the classroom varies inversely as the cost of each calculator. She can buy 24 calculators that cost $60 each. How many calculators can she buy if they cost $80 each?

A: ?

2. Jeffs builds model train layouts. He has $75 to spend on packages of miniature landscape items. He receives 6 free packages with each order. The number of packages y that Jeff can buy is given by y = 75/x + 6, where x represents the cost of each package in dollars. Describe the reasonable domain values and graph the functions.

A: Both the number of packages and the cost of each package in dollars will be nonnegative, so the nonnegative vlaues are reasonable for the domain and range.

Graph: ?


3. Suppose a cone and a cylinder have the same radius and that the slant height l of the cone is the same as the height h of the cylinder. Find the ratio of the cone's surface area to the cylinder's surface area.

Area of cone: S = πrl + πr^2

Area of cylinder: S = 2πrh + 2πr^2

Answer 1

#1 we have n calculators that cost c each.
Since nc = k is constant,
24*60 = 80n

#2
Actually, the cost must be a positive integer divisor of 75, since the number of packages must be an integer.

#3
well, you have the formulas, and you want the ratio

scone/scyl = (πrl + πr^2)/(2πrh + 2πr^2)
= πr(l+r) / 2πr(h+r)
= (l+r) / 2(h+r)