GEOMETRY
Shawn Nguyen is a mail clerk at an advertising firm. She earns $12.00 per hour. This week she worked 391/2 hours. What is her "straight-time" pay for the week?
Find the straight-time pay.
Hourly Rate • Hours Worked = Straight-Time Pay
$12.00 • 39.5 = $474.00
If (23)2 = 4p, then 3p =
27
In how many different ways can 5 students be seated in 3 chairs?
60.
5 x 4 x 3 = 60
What is the area of a circle in which a 3 by 4 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*r2
Ralph Masales is an accounting clerk. He earns $14.40 per hour. How many hours per week must he work if he wants to earn approximately $550.00 per week?
HINT: Find the straight-time pay. Let h represent the hours
Straight-time pay = Hourly Pay • Hours Worked (Given formula)
$550.00 = $14.40 • h (Substitute in given values and h for hours.)
$550.00 = $14.40 h (Rewrite without multiplication sign.)
38.19 = h (Divide $14.40 on both sides of the equation.)
When the number of people who contribute equally to a gift decreases from 4 to 3, 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 + 11/2 of its price.
How much does the event cost?
$10.00
$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-food shadow?
62.5 feet.
Proportional reasoning with similar triangles.
Alan Moore is paid $8.20 an hour for a regular -hour week as a restaurant host. His overtime rate is 11/2 times his regular hourly rate.
This week he worked his regular 40 hours + 10 hours of overtime.
What is his total pay?
Step 1: Find the straight-time pay. Hourly Rate • Regular Hours Worked
$8.20 • 40 = $328.00 straight-time pay
Step 2: Find the overtime pay. Overtime Rate • Overtime Hours Worked
(1.5 $8.20): • 10 = $120.00 overtime pay
Step 3: Find the total pay. Straight-Time Pay + Overtime Pay
$328.00 + $120.00 = $448.00 total pay
Simplify (x + 2)2 - x2
4(x+1)
NOTE: x2 + 4x + 4 - x2
3 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.
If the integer lengths of the three sides of a triangle are 4, x, and 9, what is the least possible perimeter of the triangle?
19.
In the given triangle, 9 - 4
Jessica Cooper is a receptionist at a hotel and conference center. She is paid $12.50 an hour for a regular 40-hour week. Her overtime pay is 1 2 1 times her regular hourly rate. This past week, Jessica earned $612.50 in total pay. How many hours of overtime did she work?
HINT: Total Pay = Straight-Time Pay + Overtime Pay
$612.50 = ($12.50 • 40) + [($12.50 • 1.5) • h]
$612.50 = $500.00 + $18.75h
$112.50 = $18.75h
6 = h
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.
For the system of three equations:
x - z = 7
x + y = 3
z - y = 6
What is x? (HINT: use the equation with common variables to solve the other two)
8
Five students, all of different heights, are randomly arranged in a line.
What is the probability that the tallest student will be 1st in line and the shortest student will be last in line?
1 in 20.
1 x 3 x 2 x 1 x 1 = 6
6 ways in which students can be arranged under given conditions. Under no conditions, the ways are 5 x 4 x 3 x 2 x 1 = 120.
6 in 120 = 1 in 20.
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.
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 = the number of hours Mike works alone to paint the fence, then 3x is the number of hours Bill works alone to paint the fence.
So 2(1/x) + 2(1/3x) = 1 gives x = 8/3 hours.
Fruit for a dessert costs $1.20 a pound. If 5 pounds of fruit make a dessert for 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 5/18lbs serves one person, so
24 × 185 = 4 × 35 = 320lbs
serve 24 people. Since the fruit costs $1.20 a pound, the cost of the fruit needed to serve 24 people is
20 ÷ 3 × $1.20 = 20 × $0.40 or $8.00
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.
x, y, 22, 14, 10... In this sequence, each term after the 1st 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.