Word Problems Flashcards
When you see “quotient”, what should you do?
Divide
When you see “product”, what should you do?
Multiply
When you see “difference”, what should you do?
Subtract
The difference between x and y?
x-y
m decreased by n is?
m - n
a diminished by b is?
a - b
x from y is?
y - x
m less n is?
m - n
a less than b is?
b - a
What sign means “at least”?
≥
What sign means “not more than”?
≤
What sign means “over”?
>
What sign means “under”?
<
m times the sum of q and r is?
m(q + r)
Six less the product of x and y is?
6 - xy
The difference between c and d divided by f is?
f
b less than the quotient of r divided by s is?
r/s - b
The sum of d and g is the same as the product of h and r is?
d + g = hr
x is at least y means?
x ≥ y
Zeb’s age n is not more than 21 means?
n ≤ 21
Let I = my age. I am over 30 years old. How do you write this?
I > 30
Let p = most people. Most people are under 7 feet tall.
how do you write this?
p < 7
How are ratios written?
3/5
3:5
What is the ratio of 5 ounce to 2 lbs.?
5/32
16 oz to a pound
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
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
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
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
p years ago, Mary was q years old. In r years, she will be how many years old?
q + p + r
For speed…
time = ?
distance / speed
For speed…
distance = ?
speed x time
speed = ?
distance/time
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
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
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
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
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
Which is larger: -9 or -15?
-9 is higher
A triangle’s angles total to ____ degrees.
180
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
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
If a job can be completed in x hours, ____ amount of work can be completed each hour.
1/x
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
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
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
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
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
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
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
1 foot = ___ inches
12
1 yard = ___ feet
3
1 mile = ____ feet
5,280
1 cup = ___ ounces
8
1 pint = ___ cups
2
1 quart = ___ pints
2
1 gallon = ___ quarts
4
1 pound = ____ ounces
16
1 ton = ____ pounds
2,000
1 peck = ___ dry quarts
8
1 bushel = ___ pecks
4
1 kilogram = _____ grams
1,000
1 kiloliter = _____ liters
1,000
1 kilometer = ____ meters
1,000
1 meter = _____ millimeters
1,000
1 meter = ___ centimeters
100
1 centimeter = ____ millimeters
10
