WORD PROBLEMS INVOLVING POSITIVE AND NEGATIVE INTEGERS

Problem 1 :

When Steve woke up. His temperature was 102˚F. Two hours later it was 3˚Lower. What was his temperature then?

Solution :

Steve's temperature when he woke up = 102˚F

After 2 hours it reduces 3˚F

Steve's temperature two hours later = 102 - 3

= 99˚F

Problem 2 :

An elevator is on the twentieth floor. It goes down 11 floors and then up 5 floors. What floor is the elevator on now ?

Solution :

Initial location of the elevator = 20^th floor

It goes down (↓) 11 floor. So, -11

It goes up (↑) 5 floors. So, + 5

By combining, we get

= 20 + (-11) + 5

= 25 - 11

= 14

So, now the elevator is is 14^th floor.

Problem 3 :

A deep-sea exploring ship is pulling up a diver at the rate of 25 feet per minute. The diver is 200 feet below sea level. How deep was the diver 10 minutes ago?

Solution :

The Speed of the ship pulling up the diver 25 feet per minute

Height of the diver is 200 feet below the sea level. Since it below the sea level, we take -200

Time for 10 minutes ago.

We use distance formula.

Distance = Speed × time

= 25 × 10

= 250

Since it is below the sea level, the result becomes -250.

= -200 - 250

= -450 feet deep

So, the diver was -450 feet deep 10 minutes ago.

Problem 4 :

If it is 5˚ outside and the temperature will drop 17˚ in the next six hours, how cold will it get?

Solution :

It had a temperature of 5˚

Next six hours, It goes down 17˚. So -17

Quantity of cold It will get = 5˚ - 17˚

= -12˚

So, it will be -12˚ cold.

Problem 5 :

Josie has $47 left on her checking account. If she writes a check for $55, what will Josie's balance be?

Solution :

Old balance = $47

She write the check of $55. So -55

New balance = 47 - 55

= $ -8

So, Josie's balance would be  $ -8.

Problem 6 :

Joe is playing a game with a regular die. If the number that turns up is even, he will gain 5 times the number that comes up. If it is odd, he will lose 10 times the number that come up. He tosses a 3. Express the results as an integers.

Solution :

Let x be the number.

As per question,

If x is even, then he gains 5x.

If x is odd, then he loses -10x

Then,

He tosses a 3.

3 is an odd number.

So, we use the odd -10x.

= -10(3)

= -30

Problem 7 :

It will be -12˚ tonight. The weatherman predicts it will be 25˚ warmer by noon tomorrow. What will the temperature be by noon tomorrow?

Solution : 

Tonight temperature will be -12˚.

Tomorrow noon temperature will be 25˚.

So, -12 + 25

= 13˚

So, 13˚ temperature will be the tomorrow noon.

Problem 8 :

The average temperature at the south pole is -45˚F. The average temperature on the Equator is 92˚F. How much warmer is the average temperature on the Equator than at the South Pole?

Solution : 

The average temperature at the south pole is -45˚F.

The average temperature on the Equator is 92˚F.

Find the difference in the temperature.

= 92˚F - (-45˚F)

= 92˚F + 45˚F

= 137˚F

So, the average temperature on the Equator is 137˚F warmer than at the south pole.

Problem 9 :

The elevation of Mt. Everest is 29,028 feet. The elevation of the dead sea is -485 feet. What is the difference in the elevation between Mt. Everest and the Dead Sea?

Solution : 

Height of Mt. Everest = 29,028 feet

Height of dead sea = -485 feet

Difference in two elevations = 29,028 - (-485)

= 29,028 + 485

Difference = 29513

Problem 10 :

The temperature was -3˚c last night. It is now -4˚c. What was the change in temperature?

Solution : 

Temperature last night = -3˚c.

Temperature  = -4˚c.

Change in temperature = -4˚c - ( -3˚c)

= (-4 + 3)˚c

Change in temperature = -1˚c

Problem 11 :

Before a show, there are 8 people in a theater. Five groups of 4 people enter, and then three groups of 2 people leave. Find how many people are in the theater.

Solution : 

Number of people in theater = 8

Number of groups entering = 5

Number of people in each group = 4

Number of groups going out = 3

Number of people in each group, going out = 2

Number of people in theater now = 8 + 5(4) - 3(2)

= 8 + 40 - 6

= 48 - 6

= 42

So, there are 42 people are there.

Problem 12 :

You buy foam spheres, paint bottles, and wooden rods to construct a model of our solar system. What is your total cost?

Solution : 

Number of spheres = 9 cost is $2 per spheres

Number of paints = 6 cost is $3 per paints

Number of rods = 8 cost is $1 per rods

Total cost = 9(2) + 6(3) + 8(1)

= 18 + 18 + 8

= $44

Problem 13 :

Two groups collect litter along the side of a road. It takes each group 5 minutes to clean up a 200-yard section. How long does it take to clean up 2 miles? Explain how you solved the problem

Solution : 

1 mile = 1760 yards

2 miles = 2 x 1760

= 3520 yards

For 5 minutes cleaning up 200 yard section.

Let x be the time taken

200 : 5 = 3520 : x

200/5 = 3520/x

40 = 3520/x

x = 3520/40

x = 88 minutes.