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GEOMETRY
ALGEBRA II
WORD PROBLEMS
ARITHMETIC & ALGEBRA I
MISCELLANEOUS
100

What is the perimeter of a square that has an area of 25?

20

100

If x-2 = 64, what is the value of x1/3 + x0?

3/2

100
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.
100

If (23)2 = 4p, then 3p =

27

100

In how many different ways can five students be seated in three chairs?

60 

5x4x3=60

200

What is the circumference of a circle in which a 5 by 12 rectangle is inscribed?

13𝞹. 

The length of a diagonal of a 5 by 12 rectangle is 13 (pythagorean theorem). The diagonal of the rectangle is the diameter of the  inscribed circle, so C = 2𝞹r = 𝞹(2r) =13𝞹

200

Let the function f be defined by f(x) = 3x-1 and let the function g be defined by g(x) = x2. If m is a positive number such that f(7) = g(m) + g(2), what is the value of m?

4

200
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
200
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.
200

What is the area of the circle whose radius is the average of the radii of two circles with areas of 16𝞹 and 100𝞹?

49𝞹

300

The height h of a cylinder equals the circumference of the cylinder. In terms of h, what is the volume of the cylinder?

h3/4𝞹 

h=2𝞹r, so r=h/2𝞹. 

Volume of a cylinder = 𝞹r2h = 𝞹(h/2𝞹)2h= h3/4𝞹.

300

A culture of 5000 bacteria triples every 15 minutes. What is the size of the bacteria population after 2 hours have elapsed?

32,805,000

300
The regular price of software at a computer superstore is 12% off the retail price. During an annual sale, the same software is 25% off the regular price. If the retail price is p, what is the sale price in terms of p?
0.66p. Since the regular price of software is 12% off the retail price p, the regular price of the software can be expressed as 0.88p. So the sale price is 0.75 x 0.88p = 0.66p.
300
Simplify (4a+a-3)(4b-2b-b)
5ab-3b
300
Three fair coins are tossed at the same time. What is the probability that all three coins will come up heads OR all will come up tails?
1/4. 1/8 (all heads) + 1/8 (all tails) = 1/4.
400

If the integer lengths of the three sides of a triangle are 4 cm, x cm, and 9 cm, what is the least possible perimeter of the triangle?

> 19cm. So least possible integer perimeter = 20cm

Reason:

In the given triangle, third side has to be > 5 (=9-4)

400

What is the equation of the graph obtained by shifting the graph of y=x2 horizontally to the left 4 units and vertically down 3 units?

y = (x+4)2 - 3

400
Jars A, B, and C each contain 8 marbles. What is the minimum number of marbles that must be transferred among the jars so 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?
4. 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.
400
For the system of three equations: x-z=7, x+y=3, z-y=6, what is x?
8
400
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. Under no conditions, the ways are 5x4x3x2x1=120. 6/120=1/20.
500

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. 

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.

500

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. 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.

500
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.
500
For how many integer values of b is b+3>0 and 1>2b-9?
Seven. 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.
500
x, y, 22, 14, 10... In this sequence, each term after the first term x is obtained by halving the term that comes before it and then adding 3 to that number. What is the value of x-y?
32. x=70, y=38. 70-38=32.