**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.

**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.

After having gone through the stuff given above, we hope that the students would have understood "Solving a real world problem using the distributive property".

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