**Writing and solving one step multiplication and division problems :**

In this section, we are going to see how word problems can be solved using one step multiplication division.

**Example 1 :**

When we multiply a number by 4, we get 124. Find the number.

**Solution : **

Let "x' be the required number.

According to the question, we have

4x = 124

Here "x" is multiplied by "4". To get rid of 4, we have to divide by 4 on both sides and solve the equation as explained below.

4x / 4 = 124 / 4

x = 31

Hence, the required number is "31".

**Example 2 :**

When we divide a number by 7, we get 14. Find the number.

**Solution : **

Let "m' be the required number.

According to the question, we have

m / 7 = 14

Here "m" is divided by "7". To get rid of 7, we have to multiply by 7 on both sides and solve the equation as explained below.

(m/7) x 7 = 14 x 7

m = 98

Hence, the required number is "98".

**Example 3 :**

Alex borrowed some money from Jose. After 3 years, Alex returned 2 times of borrowed money to Jose. If the returned money is $226, how much money did Alex borrow from Jose ?

**Solution : **

Let "x' be the borrowed money.

According to the question, we have

2x = 226

Here "x" is multiplied by 2. To get rid of 2, we have to divide by 2 on both sides and solve the equation as explained below.

2x / 2 = 226 / 2

x = 113

Hence, the borrowed money is $113.

**Example 4 :**

David has some money. He gave one fourth of the money to Lily. If Lily gets $8 from David, how much money did David have initially ?

**Solution : **

Let "m' be the money that David had initially.

According to the question, we have

m / 4 = 32

Here "m" is divided by "4". To get rid of 4, we have to multiply by 4 on both sides and solve the equation as explained below.

m/4 x 4 = 32 x 4

m = 128

Hence, David had $128 initially.

**Example 5 :**

In a deposit, invested money will become 4 times itself in 5 years. If Rosy receives $3280 after five years, how much money did Rosy invest ?

**Solution : **

Let "m' be the money that Rosy invested.

According to the question, we have

4m = 3280

Here "m" is multiplied by "4". To get rid of 4, we have to divide by 4 on both sides and solve the equation as explained below.

4m / 4 = 3280 / 4

m = 820

Hence, Rosy invested $820.

**Example 6 :**

Jacob has some number of candies and Michael has 35 candies. If Michael has candies 5 times as Jacob, how many candies does Jacob have ?

**Solution : **

Let "p' be the number of candies that Jacob has.

According to the question, we have

5p = 35

Here "p" is multiplied by "5". To get rid of 5, we have to divide by 5 on both sides and solve the equation as explained below.

5p / 5 = 35 / 5

p = 7

Hence, Jacob has 5 candies.

**Example 7 :**

Daniel had some hot dogs and he gave one third of the hot dogs to Alex. If Alex gets 8 hot dogs from Daniel, how many hot dogs did have initially ?

**Solution : **

Let "h" be the number of hot dogs that Daniel had initially.

According to the question, we have

m / 3 = 8

Here "m" is divided by "3". To get rid of 3, we have to multiply by 3 on both sides and solve the equation as explained below.

m/3 x 3 = 8 x 3

m = 24

Hence, Daniel had 24 hot dogs initially.

**Example 8 :**

Between the hours of 10 P.M. and 6 A.M., the temperature decreases an average of of a degree per hour. How long, in hours and minutes, will it take for the temperature to decrease by 5 °F ?

**Solution : **

Write an equation. Let x represent the number of hours it takes for the temperature to decrease by 5 °F.

(-3/4)x = -5 ----> -3x/4 = -5

Solve the equation using an inverse operation.

Multiply both sides by - 4/3.

(-4/3).(-3x/4) = -5.(-4/3)

x = 20/3 = 6 2/3

It takes 6 2/3 hours.

Convert the fraction of an hour to minutes.

2/3 hours x 60 min / 1 hr = 40 minutes

It takes 6 hours and 40 minutes for the temperature to decrease by 5 °F.

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