Q8: Word Problems A Flashcards
What do the following words translate to, in algebraic symbols?
a) is
b) of
c) per
d) percent
e) what
f) half as many
a) =
b) * (times)
c) /
d) /100
e) x (variable we are trying to find)
f) *.5
Translate the following into Algebraic Expressions or Equations:
a) There are 5 less B than A
b) x is 5 times as large as 2 less than y
c) 3x percent of y
a) B = A - 5
b) x = 5(y-2)
c) 3xy/100 (percent –> /100, of –> *)
Translate into equations:
a) James is twice as old as Mary was 2 years ago
b) If the Bus were 3 feet longer, it would be 4 times as long as the car
c) 20% more than A is 500 less than B
a) J = 2(M-2)
b) B + 3 = 4C
c) 1.2A = B - 500
Translate:
In 5 years, Adam will be twice as old as Bob.
A + 5 = 2(B + 5)
The trick here is to compare the 2 ages in the future!
A common mistake is A + 5 = 2B
Translate into equations and solve:
200 pounds of apples are divided into small and large bags, of 5 and 10 pounds respectively.
There are 4 more small bags than large bags.
How many large bags are there?
Define variables: S = small bags, L = large bags
1) 200 = 5S + 10L
2) S = L + 4
Substitute 2 into 1, so we only have one variable, L
200 = 5(L + 4) + 10L
200 = 5L + 20 + 10L
180 = 15L
L = 12
Small boxes are $3, large boxes are $5.
If John buys 10 boxes for $36, how many are small?
Solve by writing the equations, or use your own intuition and logic.
S = small, L = large
(1) S + L = 10
(2) 3S + 5L = 36
The question asks for S. So, solve (1) for L, so we can then substitute it into (2) and solve for S.
L = 10 -S
3S + 5(10 - S) = 36
- 2S + 50 = 36
- 2S = 14 –> S = 7
Intuition method: If they were all small, it would cost 10*3 = $30
Larges are $2 more than smalls, so if we swap 3 smalls for larges, it would cost $36.
What is the equation for Distance or Work?
RT = D
RT = W
R = Rate (miles per hour, jobs per day, etc)
T = time
A bus travels 720 miles at 20 miles per hour. How long does this take?
RT = D
T = D / R
T = 720 / 20 = 36 hours
Quickest way to do the division is drop the 0 and divide by 2. (divide by 10 and then 2)
John travels 480 feet in 2 minutes. What is his speed, in feet per second?
Notice the Units! We need to convert minutes to seconds.
2 minutes * 60 seconds/min = 120 seconds
RT = D
R = D/T
R = 480 / 120 = 4 ft/s
Joe jogs a 26 mile course at 4 miles per hour.
If Mary jogs the course in 90 fewer minutes, how fast did she jog?
First, find time for Joe:
Joe: T = D/R = 26 / 4 = 6.5
Mary takes 90 fewer minutes –> convert to hours –> 1.5 fewer hours –> 5 hours
Mary: R = D/T = 26 / 5 = 5.2 miles per hour
Relative Rates:
A and B are 20 miles apart at 1pm
A walks towards B at 2mph.
B walks towards A at 3mph.
What time will they reach each other?
We can add their rates together, since they are going towards each other.
Combined Rate = 2+3 = 5
T = D/R = 20/5= 4 hours
1pm + 4 hours = 5pm
A starts 35 miles west of B.
They both head east at the same time.
A travels 30mph
B travels 25mph
After how many hours will A and B meet?
Relative Rates:
They are both heading the same direction, so A is catching up to B at the difference between their speeds:
Closing Speed = 30 - 25 = 5mph
T = D/R = 35 / 5 = 7 hours
Average Rate:
Joe walks to work at 3mph, and walks home at 2mph.
What is his average speed for the entire trip?
Average Rate: Find the Total Time!
You can’t just average the 2 rates! (the reason is Joe spends more time walking at the slower rate)
You must find the total time and total distance, and then divide:
Pick a number for the distance each way, such as 6 miles:
Going: T = 6/3 = 2 hours
Return: T = 6/2 = 3 hours
Total T = 5 hours, Total D = 12 miles
R = 12/5 = 2.4 mph
Joe can sand 2/5 of the table in 6 hours.
How long will it take him to sand the whole table?
6 workers can complete 1/2 of a job in 5 days.
a) What is the rate of 1 worker?
b) How many days would it take for 2 workers to complete a full job?
a) RT = W
Let R = Rate of 1 worker
There are 6 workers, so 6R * 5 =1/2
30R = 1/2
R = 1/60 jobs/day
b) If 1 worker has a rate of 1/60, 2 workers have a rate of 2/60 = 1/30 jobs/day
Take the reciprocal to find time: 30 days
