Lesson Word Problems

Source code of 'Word Problems'

This Lesson (Word Problems) was created by by technofranchise(0)

: View Source, Show
About technofranchise: Computer System Engineer

Q.James wants to cover a floor measuring 90cm by 120cm with square tiles of the same size?
Given that he uses only whole tiles,find

(a) the largest possible length of the side of each tile 
(b) the number of tiles that are needed to cover the floor

(a) Solution:

In to take the largest possible length of the side of each tile , we have to factorize the length and the width and then, find the highest common factor(s) between them:

Factors of 90=2 X 3 X 3 X 5 => 2 X 3^2 X 5=>2 X 3 X 5=30

Factors of 120= 2 X 2 X 2 X 3 X 5=> 2^3 X 3 X 5=>2^3 X 3 X 5=> 2 X 3 X 5=30

So, the largest possible length is 30 cm.

(b) Solution:

The number of tiles that are needed to cover the floor:

No of tiles required= Total area of floor/ Area of one tile =

(Length X Width)/ (Length X Width) =>(90 X 120)/(30 X 30)= 12 cm

Q. Paul has three pieces of ropes with lenghts of 140cm,168cm,210cm.He he wishes to cut the three pieces of equal length with no remainder

a)what is the greatest possible length of each small pieces of ropes. 
b)how many smaller pieces of rope of equal length can be get altogether.

(a) Solution:

Taking the highest common factor of the three lengths 140,168,210:

*[illustration HCF.png].

2 X 7= 14 cm is the greatest possible length of each small pieces of ropes.

(b) Solution:

The number of smaller pieces of rope of equal length can be get altogether are:
 
10 + 12 + 15=37 cm

Q. Two lighthouses flash their lights every 20 seconds and 30 seconds respectively.
Given that they flash together at 8 pm, when will they next flash together?

Solution:

The least common multiple of 20 seconds and 30 seconds is 60 seconds, which means that the  lights will flash again 60 seconds after 8 pm

Q. Three bells toll at intervals of 8 minutes, 15 minutes and 24 minutes respectively.
If they toll together at 3 pm at what time will they next toll together again?

Solution:

Taking the least common multiple of the three minutes, we can determine at which time, they will toll again because that will be the common time for all these intervals.

So , LCM of 8,15,24= 2 X 3 X 2 X 2 X 5=>120 minutes or two hours

Q.Mount Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations?

Solution:

Mount Everest is 29028 above sea-level and the Dead Sea is 1312 feet below sea level.

Above sea level= +29028

Below sea level= -1312

The difference = 29028 - (-1312)=>29028+1312
=30340

Q.In Buffalo, New York, the temperature was -14�F in the morning. If the temperature dropped 7�F, what is the temperature now?

Solution:

Morning temperature=-14�F

The drop is 7�F which means that the temperature has further reduced i.e -7�F

The current temperature= -14-7=-21�F

Q. A chocolate factory usually makes 3,865 chocolates per month. In the month before Valentine's day, it makes 2,953 more than that. About how many chocolates does the factory produce in that month? Choose the better estimate.

3000 or 7000?

Solution:

The addition of 3865 chocolates per month and 2953 chocolates additional for Valentine's day is definitely greater than 3000; So , the better estimation is 7000

Q. Ron and Amanda collected 497 buttons, but they used 177 of them while fixing some jackets. About how many buttons do they have now? Choose the best estimate.

A: 500
B: 400
C: 300
D: 100

Solution:

After using 177 buttons, they are left with 497-177=327 and the nearest approximate value is :
C: 300

Q.A football team lost 5 yards and then gained 9. What is the team's progress?

Solution

For lost, use negative. For gain, use positive.

Progress = -5 + 9 = 4 yards

Q. Use distributive property to solve the problem below:

Maria bought 10 notebooks and 5 pens costing 2 dollars each.How much did Maria pay?

Solution

2 � (10 + 5) = 2 � 10 + 2 � 5 = 20 + 10 = 30 dollars

Q. The first term in a sequence of number is 2. Each even-numbered term is 3 more than the previous term and each odd-numbered term, excluding the first, is �1 times the previous term. What is the 45th term of the sequence?

Solution:

First, we have to generate a sequence of numbers:

2, 5, -5, - 2, 2, 5, -5, -2, ...

As we have noticed, the sequence repeats after the fourth term.

In order to find the 45th term, get the remainder for 45/4, which is 1

The 45th term is the same as the 1st term, which is 2

The 45th term is 2.

Q. Jeanne has $17 in her piggy bank. How much money does she need to buy a game that costs $68?

Solution:

Let x represent the amount of money Jeanne needs. Then the following equation can represent this problem:

17 + x = 68

We can subtract 17 from both sides of the equation to find the value of x.

68 - 17 = x

Since x=51, so Jeanne needs $51 to buy the game.