WORD PROBLEMS USING DISTRIBUTIVE PROPERTY WORKSHEET

Problem 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 ?

Problem 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 ?

Detailed Answer Key

Problem 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

Use distributive property. 

0.2x - 1.5  =  8.9

Step 3 : 

Add 1.5 to both sides.

0.2x  =  10.4

Divide each side by 0.2

x  =  52

So, 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. 

Problem 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

Use distributive property. 

0.08x + 160  =  3840

Step 3 : 

Subtract 160 from each side.

0.08x  =  3680

Divide each side by 0.08

x  =  46000

So, 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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