Percents and Algebra
A shirt that originally costs $80 goes on sale for a price of $45. What is the percent discount?
Percent change = ((new-old)/old) x 100
Percent change = ((45-80)/80) x 100
Percent change = (35/80) x 100
ANS: 43.75%
Is the number 192,856,432 divisible by 3, based on the divisibility rule?
Divisibility rule for 3: sum of all digits must be divisible by 3
1+9+2+8+5+6+4+3+2 = 40 / 3
ANS: Not divisible by 3
Express the following number in scientific notation: 0.0000234
2.34 x 10-5
A quarter has two sides: Heads and Tails. If you flip a quarter two times, what is the probability of getting Heads twice?
P(heads first time) x P(heads second time)
(1/2)(1/2) = 1/4
ANS: 1/4
3 workers can paint 5 houses in a week. How many houses can 12 workers paint in a week?
12 is 4 times 3 so the number of houses painted by 12 workers = 5 houses x 4 = 20 houses
Alternative: Set up a proportion
(5 houses / 3 workers) = (x houses / 12 workers)
5(12) = 3(x)
60 = 3x
x = 20
ANS: 20
What is the GCF of 24x7y4 and 9x5y7 ?
24x7y4 - 9x5y7 = 3x5y4 (8x2 - 3y3)
Simplify the square root of 88
Prime factorization of 88 = 2 x 2 x 2 x 11
= 22 x 2 x 11
OR
square root of 88 = square root 4 x square root 22
square root of 88 = 2 x square root 22
ANS: Square root of 88 = 2 square root of 22
Simplify the product of (3x3y-2)2 with (2x2y5)
(3x3y-2)2 (2x2y5)
(9x6y-4)(2x2y5)
ANS: 18x8y1
You flip a coin 5 times and it lands on Heads 5 times. What is the probability that the next flip (the 6th flip) will land on Heads as well?
ANS: 1/2
There are two triangles, A and B, that are similar. Triangle A has the following angles: 30, 60, and 90 degrees. What are the angles in Triangle B?
Similar triangles have the same angles so triangle B also has 30, 60, 90 degree angles.
Find the GCF and LCM of the following numbers: 24, 30, and 48.
24 = 2 x 2 x 2 x 3
30 = 2 x 3 x 5
48 = 2 x 2 x 2 x 2 x 3
GCF = 2 x 3 = 6
LCM = 2 x 2 x 2 x 2 x 3 x 5 = 240
ANS: GCF = 6, LCM = 240
For the number 1,503,25x, where x is the ones unit of the number, what value(s) of x would make the seven-digit number divisible by 8?
Divisibility of 8: the last three digits must be divisible by 8
25x divisible by 8
256 is divisible by 8
ANS: only when x = 6
Simplify the expression: (3.15 x 10-3) x (2.4 x 105)
3.15 x 2.4 = 7.56
10-3 x 105 = 102
ANS: 7.56 x 102
A student is about to take a final chemistry test. She currently has a class average of 80 across her first 4 tests. The final is going to be worth 2 test grades. If she wants to get an average of 85 in the class, what must she get on the final exam?
Average = (sum of all test scores / # of tests)
Sum of all test scores = average x # of tests
Current sum after 4 tests = 4 x 80 = 320 points
Desired sum = 6 x 85 = 510 points
510 - 320 = 190 points
190/2 = 95 on the final
ANS: 95
The equation, y = (4/5)x describes a proportional relationship and forms a straight line on the graph. A point with a y-coordinate of 5 lies on the line. What is the corresponding x-coordinate?
y = (4/5)x
5 = (4/5)x
5 (5/4) = x
x = 25/4
50% of 5% of a number is equal to 20. What is the number?
50% = 0.5
5% = 0.05
Let x = unknown number
(0.5)(0.05)(x) = 20
0.025x = 20
x = (20 / 0.025) = (20000 / 25) = 800
ANS: 800
A grey squirrel can run up to 20 miles per hour. How fast is that in feet per second? Round your answer to the nearest tenths place. Note that 1 mile = 5,280 feet.
(20 miles / 1 hr)( 5280 feet / 1 mile)(1 hr / 3600s)
Simplify:
(2 miles/hr)(528 feet/mile)(1hr /36s)
(2miles/hr)(44 feet/mile)(1hr/3s)
88/3 feet per second
ANS: 29.3 feet/second
Simplify the expression: 3 x 105 - 20 x 104
20 x 104 = 2.0 x 105
3 x 105 - 2.0 x 105 =
ANS: 1 x 105
What is the mean, median and mode for the following data set?
STEM: LEAF:
1 0, 1, 2, 5, 6, 7
2 2, 5, 5
Key: 1｜ 0 = 10
Data set:
10, 11, 12, 15, 16, 17, 22, 25, 25
Mean = (sum of all values / # of values)
Mean = (10+11+12+15+16+17+22+25+25) / 9
Mean = 17
Median = value in the middle when arranged in order
Median = 16
Mode = 25
In a jar, the ratio of quarters to dimes to nickels is 6:8:5 respectively. If the total value of the coins in the jar is $7.65, how many quarters, dimes and nickels are there?
6(0.25) + 8(0.1) + 5(0.05) = $2.55
$7.65/$2.55 = 3
3 x (6:8:5) = 18:24:15
quarters = 18
dimes = 24
nickels = 15
FOIL completely: (x + 2)(x - 2)(2x + 1)
(x + 2)(x - 2) = x2 - 2x + 2x - 4 = x2 - 4
(x2 - 4)(2x + 1) = (2x3 + x2 - 8x - 4)
ANS: (2x3 + x2 - 8x - 4)
A triangle has three interior angles. The largest angle is 3 times the smallest angle. The 2nd largest angle is double the smallest angle. What is the measure of the largest angle?
Let x = the smallest angle
2nd largest angle = 2x
Largest angle = 3x
Total degrees in a triangle = 180 = x + 2x + 3x
180 = 6x
x = 30
Largest angle = 3x = 3(30) = 90
ANS: 90
Solve for x if: 327 = 93x
327 = 93x
9 = 32
93x = (32)3x
(32)3x = 36x
327 = 36x
27 = 6x
x = 27/6 = 9/2
ANS: 9/2
There are 7 books you want to put in a bookshelf. A row on the shelf can only hold up to 4 books. How many different ways are there to arrange 4 books in a row?
7 x 6 x 5 x 4 = 840
There are two similar rectangles where each corresponding side of the large rectangle is double that of the smaller rectangle. What would be the ratio of the area of the smaller rectangle to that of the larger rectangle?
Area of a rectangle = length x width
Let small rectangle be 1 x 2
Area small rectangle = 2 units2
Let large rectangle be 2 x 4
Area large rectangle = 8 units2
Ratio of area of small rectangle to large is 2:8 or 1:4
ANS: 1 to 4