Word Problems Flashcards
0
Q
When you see “quotient”, what should you do?
A
Divide
1
Q
When you see “product”, what should you do?
A
Multiply
2
Q
When you see “difference”, what should you do?
A
Subtract
3
Q
The difference between x and y?
A
x-y
4
Q
m decreased by n is?
A
m - n
5
Q
a diminished by b is?
A
a - b
6
Q
x from y is?
A
y - x
7
Q
m less n is?
A
m - n
8
Q
a less than b is?
A
b - a
9
Q
What sign means “at least”?
A
≥
10
Q
What sign means “not more than”?
A
≤
11
Q
What sign means “over”?
A
>
12
Q
What sign means “under”?
A
<
13
Q
m times the sum of q and r is?
A
m(q + r)
14
Q
Six less the product of x and y is?
A
6 - xy
15
Q
The difference between c and d divided by f is?
A
f
16
Q
b less than the quotient of r divided by s is?
A
r/s - b
17
Q
The sum of d and g is the same as the product of h and r is?
A
d + g = hr
18
Q
x is at least y means?
A
x ≥ y
19
Q
Zeb’s age n is not more than 21 means?
A
n ≤ 21
20
Q
Let I = my age. I am over 30 years old. How do you write this?
A
I > 30
21
Q
Let p = most people. Most people are under 7 feet tall.
how do you write this?
A
p < 7
22
Q
How are ratios written?
A
3/5
3:5
23
Q
What is the ratio of 5 ounce to 2 lbs.?
A
5/32
16 oz to a pound
24
A board is cut into two pieces that are in the ratio of 3 to 4. If the board is 56 inches long, how long is the longer piece?
7x = 56
x = 8
4(8) = 32
25
If the sum of 3 consecutive integers is twice the smallest, then what is the smallest integer?
x + (x +1) + (x + 2) = 2x
3x + 3 = 2x
3 = -x
-3 = x
26
The sum of 5 consecutive even integers is 210. What is the sum of the smallest two?
Because there are an odd number of integers, you can divide the number by 5 to get the mean (a.k.a., the third number).
210/5 = 42
This would make the numbers 38, 40, 42, 44, & 46
38 + 40 = 78
27
The sum of four consecutive integers is -50. What is the sum of the two largest?
4x + 1 + 2 + 3 = -50
4x + 6 = -50
4x = -56
x = - 14
- 14, -13, -12, -11
- 11 - 12 = -23
28
p years ago, Mary was q years old. In r years, she will be how many years old?
q + p + r
30
For speed...
time = ?
distance / speed
31
For speed...
distance = ?
speed x time
32
speed = ?
distance/time
34
A plane leaves Indianapolis traveling west. A plan leaving 30 mph faster leaves Indianapolis traveling east. After two hours the planes are 2,000 miles apart. What is the speed of the faster plane
2000 = 2x + 2(x + 30)
2000 = 4x + 60
4x = 1940 || x= 485
515 mph
35
A car leaves Chicago at 2pm going west. A second car leaves Chicago at 5pm going 30 mph faster. At 7pm the faster car hits the slower car. The accident occurred after how many miles?
Early car: 5 hrs, speed, distance of 5(speed)
Late car: 2 hrs, speed + 30, distance of 2(speed + 30)
The distances are the same so....
5s = 2(s + 30) || 5s = 2s + 60
3s = 60 || s = 20
5(20) = 100 miles
36
Sue drives for 2 hours at 60 mph and 3 hour at 70 mph. What is her average speed
2(60) + 3(70) / 5 = 120 + 210 / 5 =
330 / 5 = 66 mph
37
Don goes 40 mph in one direction and returns at 60 mph. What is his average speed?
120 = LCD || time = distance / speed
120/40 = 3 hrs, 120/60 = 2 hrs
2(120) / 5 = 240/5 = 48 mph
38
Mike must have at least an 80 average but less than a 90 average to get a B. If he received 98, 92, and 75 on the first three tests, which grade will ensure his B?
(98 + 92 + 75 + x)
80 ≤ --------------------- < 90
4
265 + x
80 ≤ ----------- < 90
4
4(80) = 265 + x || 4(90) = 265 + x
320 = 265 + x || 360 = 265 + x
55 = x || 95 = x
55 to less than 95
39
Which is larger: -9 or -15?
-9 is higher
40
A triangle's angles total to ____ degrees.
180
41
Meg is 6 times as old as Peg. In 15 years, Meg will be 3 times as old as Peg. What is Meg's current age?
6P + 15 = 3(P + 15)
6P + 15 = 3P + 45
3P = 30
P = 10
Meg = 6(10) = 60
42
A fraction, when reduced is 2/3. If 6 is added to the numerator and 14 is added to the denominator, the fraction reduces to 3/5. The sum of the original numerator and denominator is ______.
2x + 6 3
--------- = ---
3x + 14 5
5(2x + 6) = 3(3x + 14)
10x +30 = 9x + 42
x = 12
2(12) + 3(12) = 24 + 36 = 60
43
If a job can be completed in x hours, ____ amount of work can be completed each hour.
1/x
44
Rob can do a job in 8 hours. Nan can do the same job in 4 hours. How long will it take them to do the job together?
x/8 + x/4 = 1
x/8 + 2x/8 = 1
3x/8 = 1
3x = 8
x = 2 ⅔
45
Sandy takes twice as long to do a job as Randy. They finish a job together in 3 hours. How long would it take Randy to do the job alone?
3/x + 3/2x = 1
6/2x + 3/2x = 1
9/2x = 1
9 = 2x
4.5 = x
46
Walnuts selling at $6/lb are mixed with 2 lbs of almonds costing $9/lb to give a mixture selling at $7/lb. How many pounds of walnuts were used?
6w + 9(2) = 7(w + 2)
6w + 18 = 7w + 14
4 = w
47
Water is poured into a tank at the same time a pipe is opened that drains the tank. If the tank if filled in 10 hours and the tank can empty in 15 hours - assuming the tanks starts out empty - how many hours does it take to fill the tank?
x/10 - x/15 = 1
3x/30 - 2x/30 = 1
x/30 = 1
x = 30
48
Adult tickets cost $10. Children's tickets cost $5. If 100 tickets are sold and $800 is taken in, how many adult tickets were sold?
10AT + 5(100 - AT) = 800
10AT + 500 - 5AT = 800
5AT + 500 = 800
5AT = 300
AT = 60
49
The number of quarters is four more than twice the number of dimes. If the total is $7, how many dimes are there?
10D + 25(2D + 4) = 700
10D + 50D + 100 = 700
60D = 600
D = 10
50
Deb can do a job alone in 6 hours. After working alone for 2 hours, she is joined by Sue who can do the job alone in 8 hours. They work together and finish the job. How many hours did Deb work?
d/6 + (d - 2)/8 = 1
4d/24 + (3d - 6)/24 = 1
(7d - 6)/24 = 1
7d - 6 = 24 (ADD 6 to each side)
7d = 30
d = 4 2/7
51
1 foot = ___ inches
12
52
1 yard = ___ feet
3
53
1 mile = ____ feet
5,280
54
1 cup = ___ ounces
8
55
1 pint = ___ cups
2
56
1 quart = ___ pints
2
57
1 gallon = ___ quarts
4
58
1 pound = ____ ounces
16
59
1 ton = ____ pounds
2,000
60
1 peck = ___ dry quarts
8
61
1 bushel = ___ pecks
4
62
1 kilogram = _____ grams
1,000
63
1 kiloliter = _____ liters
1,000
64
1 kilometer = ____ meters
1,000
65
1 meter = _____ millimeters
1,000
66
1 meter = ___ centimeters
100
67
1 centimeter = ____ millimeters
10
