Download Word Problem Examples

Unit 3 --- Word Problems
Thursday, July 02, 2009
11:19 AM
Here's some good examples of Word Problems that you might run into in the home work!!
Sides of a triangle
The measures of three sides of a triangle are consecutive odd integers. The perimeter of the triangle is
57. What are the measures of the three sides?
So what do I need to do….
First thing to realize is that the three sides are consecutive
odd integers so
o
If I add 2 to the first I get the second and
o
If I add 4 to the first I get the third.
So
n = first integer
n+2 = second integer
n+4 = third integer
And since the perimeter is the sum of the sides and it equals 57
The equation is:
1st + 2nd + 3rd = 57
n + (n+2) + (n+4) = 57
Now solve it
3n + 6 = 57
3n + [6 -6] = [57-6]
3n = 51
3n/3 = 51/3
n = 17
So n = 1st side = 17; n+2 = 2nd side = 19; n+4 = 3rd side = 21
Find the percentage problems
Joe purchased a new kayak on sale for 40% off. The original price was $1362.50 If the sales tax rate is
6% how much tax would he pay. What would the final cost of the kayak be?
Find the sale price of the kayak
Original price * % off = sales price
$1362.50 * .40 = $545.00
Find the sales tax first.
sales tax = price * tax rate
S = $ 545.00 * 6%
S = $ 545.00 * .06
S = $32.70
Now find the total cost
Total cost = price + sales tax
C = $545.00 + $32.70
C= $577.70
Rate Problems
John lives in Greensboro while his brother Dennis lives in Wilmington they live 210 miles apart. On
Saturday morning they plan to meet each other They both leave there homes at 9:00 AM. John drives
at 50 miles per hour while Dennis drives at 60 miles per hour. How long will it be before they meet
each other?
First thing to realize is that they will travel the same amount of time: t hours
Second the distance traveled by each is:
o
John travels a distance of: 50t
o
Dennis travels a distance of: 55t
o
And the total distance they travel is: 210 miles
So the equation that represents the problem is:
John's distance + Dennis's distance = Total Distance
50t
+
55t
= 220
No solve for t
105t = 210
105t/105 = 210/105
t = 2 hours
Chicago and Charlotte are 521 miles apart. A freight train leaves Chicago heading to Charlotte at the
same time a high speed passenger train leaves Charlotte towards Chicago traveling 50 mph faster that
the freight. If both trains pass each other 3.3 hours later what's the speed of each train (to the nearest
whole number). How far did each train travel.
First thing to do is let
x = the speed of the freight train
x+50 = speed of the passenger train
And the distance each train travels is equal to
distance = "it's speed" * "time it travels"
Freight distance = 3.3x
Passenger dist. = 3.3(x + 50)
Total distance = Freight distance + Passenger distance
521 = 3.3x + 3.3(x+50)
Solve
521 = 3.3x + 3.3(x+50)
521 = 3.3x + 3.3x + 165
521 = 521 6.6x + 165
521 - 165 = 6.6x + 165 - 165
356 = 6.6x
356/6.6 = 6.6x/6.6
53.9394 = x
x= 54 ----- freight train speed
x+50= 104 --- passenger train speed.
How far did each train travel?
distance = speed * time
Freight:
d = 54(3.3) = 178.2
Passenger: d = 104(3.3) = 343.2
Work problems
Crane A can unload a cargo ship in 10 hours and crane B can unload it in 14 h. How long will it take the
two cranes to unload the ship working together? Round to the nearest tenth.
First thing to realize is that is a rate problem.
If it takes Crane A 10 hours to do the job then it works at a rate of 1/10 of the
job per hour.
If it takes Crane B 14 hours to do the job then it works at a rate o 1/14 of the
job per hour.
If it takes x hours to complete the job working together then:
Crane A + Crane B = total job = 1
(1/10)*x + (1/14)*x = 1
Solve it:
x/10 + x/14 = 1
(14/14) * x/10 + (10/10) * x/14 = 1
14x/140 + 10x/140 = 1
24x/140 = 1
(140) (24x/140) = (1)(140)
24x = 140
24x/24 = 140/24
x = 5.8 hours
----- Get common denominators.