When we talk about the elementary branch of Mathematics, performing an arithmetic operation comes into consideration. All these arithmetic operations are addition, subtraction, multiplication, and lastly, division. These arithmetic operations are applicable to several kinds of numbers, one of which is integers. Integers tend to form a special group of numbers which means that they do consist of a decimal or a fractional part.
These integers include all the positive numbers, the negative numbers and zero. Well, the arithmetic operations that we perform on the integers are the same as the ones on the whole numbers. We know that integers can either be a positive or a negative number, that is, they either have a positive (+) or a negative (-) sign preceding them.
However, this can often make them quite confusing. Hence, they tend to differ from the whole numbers. Let us take a look at how we can perform different arithmetic operations on integers. Given below are the integer problems and answers which also includes the negative number word problems.
Example 1: Determine two consecutive integers in a way that their sum is equal to 129.
Let x and x + 1 be the two numbers. (Note that the consecutive integers differ by 1)
We know that their sum is equal to 129. Hence, we can write the equation as x + (x + 1) = 129
Solving for x, we get,
x = 64
Hence, the two integers are x = 64 and x + 1 = 65
When we check, we get the sum of the two numbers 129.
Example 2: The sum total of three consecutive even integers is found to be 84. Determine the integers.
We know that the difference between the two even integers is 2.
Hence, x, x + 2 and x + 4 would be the three numbers.
Their sum total is equal to 84
Hence we can say that
x + (x + 2) + (x + 4) = 84
When we solve for x we get the three numbers
x = 26 , x + 2 = 28 and x + 4 = 30
We can see that the three numbers are even and that their sum is 84.
Example 3: The sum of the first and third of the total of three consecutive odd integers is found to be 131 less than what is three times the second integer. What are the three integers?
Let us assume x, x + 2 and x + 4 to be three integers.
The sum of the first x and third x + 4 can be given by x + (x + 4)
Also, 131 less than three times the second 3(x + 2) is given by 3(x + 2) - 131
Since the sum of the first and third integer is 131 less than three times the second integer, it gives us,
x + (x + 4) = 3(x + 2) - 131
When we solve for x we can find all the three numbers
x = 129 , x + 2 = 131 , x + 4 = 133
Example 4: Determine the four consecutive even integers in such a way that the sum of the first two integers added to twice the sum of the last two integers is 742.
Let us consider x, x + 2, x + 4 and x + 6 to be the four different integers.
The sum of the first two integers is x + (x + 2)
The twice the sum of the last two integers can be written as
2 ((x + 4) + (x + 6)) = 4 x + 20
Then the sum of the first two integers added to twice the sum of the last two integers equalling 742 can be written as
x + (x + 2) + 4 x + 20 = 742
When we solve for x, we can find all the four numbers
x = 120 , x + 2 = 122 , x + 4 = 124 , x + 6 = 126
We can see that the sum of the first two integers, when added to twice the sum of the last two integers, gives us 742.
Example 5: A submarine submerges into the sea at the rate of 5 m/min. If it descends from a distance of 20 m above the sea level, how much time will it take in reaching 250 m below the sea level?
It is given that,
The initial position = 20 m (above the sea level)
The final position = 250 m (below the sea level)
Hence, the total depth it submerged is equal to
= (250+20) = 270 m
Therefore, the submarine travelled a distance of 270 m below the sea level.
The time taken to submerge 1 meter = 1/5 minutes
Hence, the time taken to submerge 270 m would be
= 270 × 1/5 = 54 min
Therefore, the submarine would reach a distance of 250 m below the sea level in 54 minutes.