GEOMETRY
If 1/3 of a number is 4 less than 1/2 of the number, the number is
24. Let x represent the unknown number. Since 1/3 of x is 4 less than 1/2 of x, x/3 = x/2 - 4. So, 2x = 3x - 24, giving x = 24.
When the number of people who contribute equally to a gift decreases from four to three, each person must pay an additional $10. What is the cost of the gift?
$120
The cost of admission to an event is $5.00 plus one half of its price. How much does the event cost
$10.00 Because $5 + 0.5($10) = $10.
At a certain time of day, a 25-foot telephone pole casts a 10-foot shadow. At that same time, how high would a tree have to be in order to cast a 25-foot shadow?
62.5 feet. Proportional reasoning with similar triangles.
A culture of 5000 bacteria triples every 15 minutes. What is the size of the bacteria population after 2 hours have elapsed? (Calculator needed.)
32,805,000
Susan weighs p pounds. If Susan gains 17 pounds, she will weigh as much as Carol, who weighs 8 pounds less than Judy. If Judy weighs x pounds, then Susan's weight, p, in terms of x is
x-25
If (2^3)^2 = 4^p, then 3^p =
27
In how many different ways can five students be seated in three chairs?
60. 5x4x3=60
What is the area of a circle in which a 6 by 8 rectangle is inscribed?
25pi. The length of a diagonal of a 6 by 8 rectangle is 10 (pythagorean theorem). The diagonal of the rectangle is the diameter of the circle inscribed, and A = pi*r^2
Let the function f be defined by f(x) = 3x-1 and let the function g be defined by g(x) = x^2. If m is a positive number such that f(7) = g(m) + g(2), what is the value of m?
4
A boat moored in Richardson Bay (Sausalito) has a ladder that hangs down from the deck of the boat and touches the flat sea surface. The rungs are 1 foot apart. At low tide, ten rungs of the ladder are exposed. At high tide, the water level rises 6 feet. How many of the rungs will remain exposed (assume the boat doesn't rise)?
4 rungs will be exposed.
Simplify (x + 2)^2 - x^2
4(x + 1), or 4x + 4 is acceptable
What is the area of a cone with a height of 5 and a radius of 3?
15pi
Fruit for a dessert costs $1.20 a pound. If 5 pounds of fruit are needed to make a dessert that serves 18 people, what is the cost of the fruit needed to make enough of the same dessert to serve 24 people
$8.00. If 5 pounds of fruit serve 18 people, then 5/18 pound serves one person, so 24 x 5/18 = 20/3 pounds. Since the fruit costs $1.20 a pound, the cost of the fruit needed to serve 24 people is 20/3 x $1.20 = $8.00.
Five students, all of different heights, are randomly arranged in a line. What is the probability that the tallest student will be first in line and the shortest student will be last in line?
1/20. 1x3x2x1x1=6, 6 ways in which students can be arranged under given conditions.
What is the number of sides of a polygon in which the sum of the degree measures of the interior angles is 4 times the sum of the degree measures of the exterior angles?
10. The sum of the degree measures of exterior angles is 360. S = (n-2)180 = 4 x 360, where n=number of sides. Solving for (n-2) = 8 or n=10.
Working alone, Bill takes three times the amount of time to paint a fence that Mike takes. If Bill and Mike work together, they can paint the fence in 2 hours. If Mike works at the same rate as when he worked with Bill, how long would it take Mike working alone to paint the same fence?
2 hours and 40 minutes. 8/3 hours acceptable. If x represents the number of hours it takes Mike working alone to paint the fence, then 3x is the number of hours it takes Bill working alone to paint the fence. So 2(1/x) + 2(1/3x) = 1 gives x=8/3 hours.
Jars A, B, and C each contain 8 marbles. What is the difference between the number of marbles in jar C and A after transfers occur such that the ratio of the number of marbles in jar A to the number in jar B to the number in jar C is 1:2:3?
8. Since jars A, B, and C each contain 8 marbles, there are 24 marbles in the three jars. Let x, 2x, and 3x represent the new numbers of marbles in jars A, B, and C, respectively. Hence, x + 2x + 3x = 24 or 6x = 24, so x=4, and 3x - x = 2x = 8.
For how many integer values of b is b+3>0 and 1>2b-9?
7. b>-3, and b<5. Since b is an integer, b may be equal to any of the following: -2, -1, 0, 1, 2, 3, or 4.