**Write variable equations :**

When writing equations, we use variables to represent the unspecified numbers or measures referred to in the problem. Then write the verbal expressions as algebraic expressions.

Some verbal expressions that suggest the equals sign are listed below.

is, is equal to, is as much as, equals, is the same as, is identical to

We use the following four steps to represent to solve any word problem.

**Step 1 :**

**Explore the problem :**

To solve a verbal problem, first read the problem carefully and explore

what the problem is about.

- Identify what information is given.
- Identify what we are asked to find.

**Step 2 :**

**Plan the solution :**

One strategy we can use to solve a problem is to write an equation. Choose a variable to represent one of the unspecific numbers in the problem.

This is called the defining a variable. Then use the variable to write expressions for the other unspecified numbers in the problem.

**Step 3 :**

**Solve the problem :**

Solve for unknown.

**Step 4 :**

**Examine the solution :**

Check answer in the context of the original problem.

- Does our answer make sense?
- Does it fit the information in the problem?

Let us see some example problems to understand how to write variable equations.

**Example 1 :**

The first ice cream plant was established in 1851 by Jacob Fussell. Today, 2,000,000 gallons of ice cream are produced in the United States each day. In how many days can 40,000,000 gallons of ice cream be produced in the United States?

**Solution :**

**Step 1 :**

**Given information :**

Quantity of ice cream to be produced.

**What do we have to find ?**

No of days required to produce the given quantity of ice cream.

**Step 2 :**

Let "T" be the required number of days to produce 40,000,000 gallons of ice cream.

Quantity of ice cream produced in each day = 2,000,000 gallons

2,000,000 x T = 40,000,000

**Step 3 :**

Divide by 2,000,000 on both sides,

T = 40,000,000/2,000,000

T = 20

**Step 4 :**

Apply T = 20 in the equation, we get

2,000,000 x 20 = 40,000,000

40, 000, 000 = 40,000,000

**Example 2 :**

Misae has $1900 in the bank. She wishes to increase her account to a total of $3500 by depositing $30 per week from her paycheck. Will she reach her savings goal in one year?

**Solution :**

**Step 1 :**

**Given information :**

Misae has $1900 in the bank.

She wishes the total amount to be $3500

She wants to deposit $30 per week.

**What do we have to find ?**

Will she reach her savings goal in one year?

For this we need to find the number of weeks required to reach the total amount of $3500.

**Step 2 :**

Let "T" be the required number of weeks

1900 + 30T = $3500

**Step 3 :**

Subtract 1900 on both sides

1900 - 1900 + 30T = 3500 - 1900

30T = 1600

Divide by 30 on both sides

30T/30 = 1600/30

T = 53.33

**Step 4 :**

Apply T = 53.33 in the equation, we get

1900 + 30(53.33) = $3500

1900 + 1599.9 = $3500

$3499.99 ≈ $3500

**Example 3 :**

Mrs. Patton is planning to place a fence around her vegetable garden. The fencing costs $1.75 per yard. She buys f yards of fencing and pays $3.50 in tax. If the total cost of the fencing is $73.50, write an equation to represent the situation.

**Solution :**

**Step 1 :**

**Given information :**

Cost of fencing per yard = $1.75

Tax = $3.50

Total cost of fencing = $73.50

**What do we have to find ?**

Total number of yards to be fenced around the vegetable garden.

**Step 2 :**

Let "y" be the required number of weeks

1.75y + 3.50 = $73.50

**Step 3 :**

Subtract 3.50 on both sides

1.75y + 3.50 - 3.50 = 73.50 - 3.50

1.75Y = 70

Divide by 1.75 on both sides

1.75y/1.75 = 70/1.75

y = 40

**Step 4 :**

Apply y = 40 in the equation, we get

1.75 (40) + 3.50 = $73.50

70 + 3.50 = 73.5

73.50 = 73.50

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