ABSOLUTE VALUE IN REAL LIFE SITUATIONS

Problem 1 :

David uses his online music store gift card (given below) to buy an album of songs by his favorite band.

Find the negative number that represents the change in the balance on David's card after his purchase.

Explain how absolute value would be used to express that number in this situation.

Solution :

Step 1 :

Lett us find the negative integer that represents the change in the balance. That is -$10.

The balance is decreased by $10, so use a negative number.

That is, the balance changed by -$10.

Step 2 :

Use the number line to find the absolute value of -$10.

–10 is 10 units from 0 on the number line.

The absolute value of -$10 is $10, or | -10 | = 10.

Step 3 :

Use the absolute value to describe the change in David's balance.

The balance on David's card decreased by $10.

Problem 2 :

You have the balance of $1500 in your bank account. You are withdrawing $500 for personal use.

Find the negative number that represents the change in the balance on  after withdrawal.

Explain how absolute value would be used to express that number in this situation.

Solution :

Step 1 :

Lett us find the negative integer that represents the change in the balance. That is -$500.

The balance is decreased by $500, so use a negative number.

That is, the balance changed by -$500.

Step 2 :

Use the number line to find the absolute value of -$500.

–500 is 500 units from 0 on the number line.

The absolute value of -$5000 is $500, or | -500 | = 500.

Step 3 :

Use the absolute value to describe the change in your account balance.

The balance on your account will be decreased by $500.

Problem 3 :

At 12 am the temperature was 0° F. By 4 am the temperature dropped to five degrees below zero.

a) Write an integer to represent the 4 am temperature.

b) Find the absolute value of this integer to determine the distance from zero.

| | = ____

Solution :

a) The temperature is at 12 am = 0° F

The temperature is at 4 am = 0° F - 5° F

So, the temperature is -5° F.

b) Distance from 0 to -5 is 5 units

|-5| = 5

Problem 4 :

Sally is running marathon. After running thirteen miles, she stops to rest.

a) Write an integer to represent the distance she ran _______

b) Find the absolute value in this integer to determine the distance it from zero. 

|  | = ___

Solution :

a) Distance ran: Moving forward adds distance, which is represented by a positive integer.

Problem 5 :

Jack owes $63 on his credit card.

a) Write an integer to represent the amount he owes ______

b) Find the absolute value in this integer to determine the distance it from zero. 

|  | = ___

Solution :

a) He owes 63, then + 63

b) Distance from 0 is 63

|63| = 63

Problem 6 :

Write integers for real life situations.

a) a gain of 5 yards on the first down.

b) 6 feet below sea level.

c) a temperature of 10 degrees below zero.

d) a $35 withdrawal.

Solution :

a) a gain of 5 yards on the first down = -5

b) 6 feet below sea level = -6

c) a temperature of 10 degrees below zero = -10

d) a $35 withdrawal = -35

Problem 6 :

Use a number line :

a) increase -2 by 5.

b) decrease -1 by 4.

c) increase -5 by 1

d) decrease 3 by 4.

Solution :

a) increase -2 by 5.

To increase -2 by 5, we move along the number line 5 units to the right. The result is +3.

b) decrease -1 by 4.

To decrease -1 by 4, we move along the number line 4 units to the left. The result is -5.

c) increase -5 by 1

To increase -5 by 1, we move 1 unit to the right, then the result is -4.

d) decrease 3 by 4.

Decreasing 3 by 4 units, move 4 units left of 3

Then 3 - 4 ==> -1

Problem 7 :

Rolls of tape must be made to a certain length. they must contain enough tape to cover between 400 feet and 410 feet. If l is the length of a roll of tape that meets this requirement, which of the following inequalities expresses the possible values of l ?

a) |l - 400| < 10    b) |l - 405| > 5     c) |l + 405| < 5

d) |l - 405| < 5

Solution :

The midpoint of 400 and 410 is the average 

= (400 + 410)/2

= 405

The midpoint is 5 away from the boundaries of the accepted range for the length of a roll of tape. So, whatever l is, it must be within 5 of the midpoint

|l - 405| < 5

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