SOLVING A REAL WORLD PROBLEM USING THE DISTRIBUTIVE PROPERTY

About "Solving a real world problem using the distributive property"

Solving a real world problem using the distributive property :

In this section, we are going to see, how distributive property can be used to solve real world problems. 

Solving a real world problem using the distributive property - Examples

Example  1 :

A family had their bill at a restaurant reduced by $7.50 because of a special discount. They left a tip of $8.90, which was 20% of the reduced amount. How much was their bill before the discount ?

Solution : 

Step 1 :

Let "x" be the bill amount before the discount. 

Then, amount to be paid after the discount $7.50 is 

=  x - 7.5

So, the reduced amount is (x - 7.5).

Step 2 : 

20% of the reduced amount is the tip $8.90.

So, we have 

0.2(x-7.5)  =  8.9

0.2x - 1.5  =  8.9

Step 3 : 

Use inverse operations to solve the equation.

Add 1.5 to both sides.

aaaaaaaaaaaaaaaaaaa 0.2x - 1.5  =  8.9 aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaa+ 1.5    + 1.5 aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa ------------------- aaaaaaaaaaqaaaaa aaaaaaaaaaaaaaaaaaa 0.2x          = 10.4 aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa ------------------- aaaaaaaaaaaaaaaaa

Since we have one digit after the decimal on both sides, multiply both sides by 10 to avoid decimal.

10(0.2x)  =  10(10.4)

2x  =  104

Divide both sides by 2. 

2x / 2  =  104 / 2

x  =  52

Hence, the family’s bill before the discount was $52.00.

Justify and Evaluate :

$52.00 - $7.50  =  $44.50

0.2($44.50)  =  $8.90. 

This is the amount given by the family as a tip. So, the answer is reasonable. 

Example  2 :

The members of a club spend 8% of their budget on entertainment. Their total budget for this year is $2,000 more than last year, and this year they plan to spend $3,840 on entertainment. What was their total budget last year ?

Solution : 

Step 1 :

Let "x" be the total budget last year. 

Then, total budget for this year is

=  x + 2000

Step 2 : 

This year, they plan to spend $3,840 on entertainment. 

Usually, they spend 8% of their budget on entertainment. 

So, we have

8% of the total budget for this year  =  3,840

0.08(x + 2000)  =  3840

0.08x + 160  =  3840

Step 3 : 

Use inverse operations to solve the equation.

Add 160 to both sides.

aaaaaaaaaaaaaaaaa 0.08x - 160  =  3840 aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaa  + 160      + 160 aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa ----------------------- aaaaaaaaaaqaaaa aaaaaaaaaaaaaaaaa 0.08x           =   3680 aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa ----------------------- aaaaaaaaaaaaaaa

Since we have two digits after the decimal in 0.08x, multiply both sides by 100 to avoid decimal.

100(0.08x)  =  100(3680)

8x  =  368000

Divide both sides by 8. 

8x / 8  =  368000 / 8

x  =  46000

Hence, the total budget for the last year was $46,000. 

Justify and Evaluate :

$46,000 + $2,000  =  $48,000

0.08($48,000)  =  $3,840 

This is the amount planned on entertainment for this year. So, the answer is reasonable. 

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