Word problems on integers

                                                       

                                                        

  Mrs. Nair opts for a mobile phone offer that charges a monthly fee of Rs 

250  plus a charge of Rs 1.25 per minute for  local calls.

She fixes a budget of Rs 400 per month for her mobile phone bill. At most 

how many minutes can she use the phone (local) each month while staying 

within her budget? [ASSET QUESTION  CLASS VII]

                  a)   100                                                                b)   110

                  c)   120                                                                    d)   150

ANSWER

        c)   120  minutes

                        She opts for mobile phone offer that charges a monthly of Rs 250

                                                    she has a budget  of her phone bill =Rs 400

                                                    Therefore , the remaining money  for local calls,

                                                                                                     400-250  =  150

                                                                charge for 1 minute local call =1.25

                                                with Rs 150  ,

                                                                she can  use the phone  = 150/1.25

                                                                                                               = 120 minutes

                                                                                                            

 An elevator descends into a mine staff  at the rate  of 6 m/min.  If the 

descends starts from 10m above the ground level, how long will it take to 

reach  -350m? 

[NCERT - PRACTICE WORKBOOK    - CLASS VII]

                      a)1 hour                                                    b)1 1/2 hour

 

                      c)2 hours                                                   d)3 hours

                 

                        

ANSWER

        a) 1 hour

              Given an elevator descends starts from 10m above the ground level  i. e , +10m

                      In one minute elevator descends 6m. 

                            distance = -350-10

                                           = -360

                                         

                         speed = distance 

                                        time

                        therefore time =  distance

                                                    speed

                                               = -360/6

                                              = -60 minute(since time is positive)

                                              = 1 hour

                                                         

 At Srinagar  temperature was -5 degree Celsius on Monday and then  it 

dropped by 2 degree Celsius on Tuesday . What was the temperature of 

Srinagar  on Tuesday? On Wednesday, it rose by 4 degree Celsius. What  was 

temperature on this day?

 [NCERT - PRACTICE WORKBOOK    - CLASS VII]

                     a)-7 degree C; -8 degree C                                   b)-5 degree C; -3degree C

                    c)-7 degree C; -3 degree C                                    d)-5 degree C; -7degree

ANSWER

                   c) -7 degree C ;-3 degree C

            on Monday it is -5 degree Celsius

            on Tuesday it is dropped by 2 degree Celsius i.e, -2 degree Celsius

                                              so -5 +(-2) = -7

           on Wednesday it is raised by 4 degree Celsius i.e, +4 degree Celsius

                                             So -7+4 = -3

         so option c is the correct answer

Q. A plane  is flying  at the height of 5000m above the sea level .At a 

particular point, it is exactly above a submarine floating 1200m below the sea 

level. What  is the vertical distance between them? [NCERT - PRACTICE  

WORKBOOK    - CLASS VII]

                   a)5200m                                                                  b)6200m

                   c)6700m                                                                  d)7200m

ANSWER; 

b) 6200 m

       Flight is  above the sea level so it is +5000m 

      Submarine floating is below the sea level and it is - 1200m

                 vertical distance between them = 5000- (-1200) m

                                                                   = 6200m

Q. A rock climber started at 500m and came a distance of 150 m down the 

rockface. How far above sea level was he then?

              a)250 m                                                        b) 300m

            c) 350 m                                                          d)400 m

ANSWER:  

        C) 350m

 Given

Rock climber starts from 500 m and came down at a distance of 150m

                      so distance = 500 - 150m

                                         = 350m

QUESTION

A submarine is at a depth of -120 meters below sea level. It rises 80 meters 

and then descends 50 meters. What is the new depth of the submarine?

ANSWER

 To find the new depth of the submarine, we need to add the changes in depth. 

The submarine initially starts at -120 meters and rises 80 meters, which can be 

represented as -120 + 80 = -40.

 Then, it descends 50 meters, so we subtract 50 from the previous result: 

    -40 - 50 = -90.

Therefore, the new depth of the submarine is -90 meters.

QUESTION

 A football team gains 10 yards on one play and loses 5 yards on the next 

play. If they repeat this pattern for a total of 6 plays, what is their net yardage?

ANSWER

 To find the net yardage, we need to calculate the total yards gained and subtract 

the total yards lost. 

The team gains 10 yards on each play, so the total yards gained are 10 * 6 = 60. 

They lose 5 yards on each play, 

        so the total yards lost are 5 * 6 = 30.

Net yardage = Total yards gained - Total yards lost 

                     = 60 - 30

                      = 30 yards.

Therefore, their net yardage is 30 yards.

QUESTION

A temperature is recorded as -5 degrees Celsius. If it decreases by 8 degrees 

Celsius, what is the new temperature?

ANSWER

To find the new temperature, we need to subtract the decrease from the initial 

temperature. 

The initial temperature is -5 degrees Celsius, and it decreases by 8 degrees 

Celsius,

 so the new temperature can be calculated as -5 - 8 = -13 degrees Celsius.

Therefore, the new temperature is -13 degrees Celsius.



QUESTION

A car starts at an elevation of 300 meters above sea level and descends 150 

meters. What is the car's new elevation?

ANSWER

 To find the new elevation, we need to subtract the descent from the initial 

elevation. 

The initial elevation is 300 meters, and the car descends 150 meters. 

So, the new elevation can be calculated as 300 - 150 = 150 meters.

Therefore, the car's new elevation is 150 meters.

QUESTION

A withdrawal of $200 is made from a bank account with a balance of $500. 

What is the new balance?

ANSWER

To find the new balance, we need to subtract the withdrawal amount from the initial balance. 

The initial balance is $500, and $200 is withdrawn. 

So, the new balance can be calculated as $500 - $200 = $300.

Therefore, the new balance is $300.

QUESTION

A submarine is at a depth of -250 feet below sea level. If it ascends 150 feet 

and then descends an additional 80 feet, what is its new depth?

ANSWER

 To find the new depth of the submarine, we need to add the ascents and descents. 

The submarine starts at a depth of -250 feet, ascends 150 feet, and then descends 

80 feet.

 So, the new depth can be calculated as -250 + 150 - 80

  

                                                                = -180 feet.

Therefore, the submarine's new depth is -180 feet.

QUESTION 

A football team gains 6 yards on one play and loses 12 yards on the next 

play. If they repeat this pattern for a total of 5 plays, what is their net yardage?

ANSWER

 To find the net yardage, we need to calculate the total yards gained and subtract 

the total yards lost. 

The team gains 6 yards on each play, so the total yards gained are 6 * 5 = 30. 

They lose 12 yards on each play, so the total yards lost are 12 * 5 = 60.

Net yardage = Total yards gained - Total yards lost 

                    = 30 - 60 

                    = -30 yards.

Therefore, their net yardage is -30 yards.

QUESTION

A temperature is recorded as -10 degrees Celsius. If it increases by 15 

degrees Celsius, what is the new temperature?

ANSWER

To find the new temperature, we need to add the increase to the initial temperature. 

The initial temperature is -10 degrees Celsius, and it increases by 15 degrees 

Celsius, 

so the new temperature can be calculated as -10 + 15 

                                                          = 5 degrees Celsius.

Therefore, the new temperature is 5 degrees Celsius.

QUESTION

A submarine is at a depth of -200 meters below sea level. If it ascends 150 meters 

and then descends an additional 100 meters, what is its new depth?

ANSWER

 To find the new depth of the submarine, we need to add the ascents and descents. 

The submarine starts at a depth of -200 meters, ascends 150 meters, 

and then descends 100 meters. 

So, the new depth can be calculated as -200 + 150 - 100 

                                                              = -150 meters.

Therefore, the submarine's new depth is -150 meters.

NOTE;

Remember to carefully consider the operations (addition, subtraction) and the 

signs (positive, negative) associated with the given quantities in order to arrive at 

the correct solution. These additional examples should provide further practice in 

solving word problems involving integers.

SUMMARY

Word problems involving integers require careful consideration of positive and 

negative values in various scenarios. Here is a summary of key points to 

 when solving word problems on integers:

 1.Addition:

When adding two positive integers, the sum is positive.

When adding two negative integers, the sum is negative.

When adding a positive and a negative integer, subtract the smaller absolute value 

from the larger and use the sign of the integer with the larger absolute value.

2. Subtraction:

Subtracting a positive integer is equivalent to adding its negative.

Subtracting a negative integer is equivalent to adding its positive.

When subtracting a positive integer from a negative integer, follow the rules of 

addition.

3. Multiplication:

The product of two integers with the same sign is positive.

The product of two integers with different signs is negative.

4. Division:

The quotient of two integers with the same sign is positive.

The quotient of two integers with different signs is negative.

5. Comparisons:

To compare two integers, pay attention to their signs and magnitude (absolute value).

The larger the absolute value, the farther the integer is from zero. A larger absolute 

value does not always mean a larger number.

6. Practice:

Practice solving word problems involving integers to reinforce the understanding of 

operations and signs.

Pay attention to the context of the problem and identify the appropriate mathematical operation to apply.

By keeping these principles in mind and practicing regularly, you can develop 

confidence in solving word problems involving integers effectively. Remember to 

carefully analyze the given information and apply the appropriate operations to 

arrive at the correct solution.