WRITING EQUATIONS

An equation is a mathematical sentence with an equal sign. To translate a word sentence into an equation, choose a variable to represent one of the unspecified numbers or measures in the sentence. This is called defining a variable. Then use the variable to write equations for the unspecified numbers.

In the following examples 1-4, translate each sentence into an equation.

Example 1 :

Twice a number increased by fourteen is identical to fifty.

Solution :

Let x be the number.

Equation :

2x + 14 = 15

Example 2 :

Half the sum of seven and a number is the same as the number decreased by two.

Solution :

Let y be the number.

Equation :

(1/2)(7 + y) = y - 2

Example 3 :

The quotient of m and n equals four more than one-third the sum of m and n.

Solution :

Equation :

m/n = (1/3)(m + n) + 4

Example 4 :

The cube of x plus the square of y is equal to fifty two.

Solution :

Equation :

x³ + y² = 52

Consecutive Numbers

Consecutive Integers :

......., -3, -2, -1, 0, 1, 2, 3, .......

n, n + 1, n + 2 are three consecutive integers if n is an integer.

Consecutive Even Integers :

......., -6, -4, -2, 0, 2, 4, 6, .......

n, n + 2, n + 4 are three consecutive integers if n is an even integer.

Consecutive Odd Integers :

......., -5, -3, -1, 0, 1, 3, 5, .......

n, n + 2, n + 4 are three consecutive integers if n is an odd integer.

In the following examples 5-6, write an equation to represent the given relationship between integers.

Example 1 :

The sum of four consecutive integers is -54,

Solution :

Let x be the first integer.

Then, the remaining three integers are

x + 1, x + 2 and x + 3

Equation :

x + (x + 1) + (x + 2) + (x + 3) = -54

Example 2 :

The product of three consecutive odd integers is 693.

Solution :

Let y be the first integer.

Then, the remaining two integers are

y + 2 and y + 4

Equation :

y(y + 2)(y + 4) = 693

Example 3 :

8 less than the sum of two consecutive integers is equal to 55.

Solution :

Let x be the first integer.

Then, the second integer is x + 1.

Equation :

x + (x + 1) - 8 = 55

Example 4 :

5 more than the product of two consecutive integers is equal to 25.

Solution :

Let y be the first integer.

Then, the second integer is y + 1.

Equation :

y(y + 1) + 5 = 25

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