# WRITING VARIABLE EQUATIONS FROM WORD PROBLEMS

To write a variable equation, we need to understand given situation.

The following keys will be helpful to convert the given words as equation.

 SumMore thanIncreasedGreater thanPlusAdded to Addition (+) DifferenceLess thandecreasedfewer thanminussubtractedless Subtraction (-) Producttimesof Multiplication (x) divided byquotient Division (/)

Problem 1 :

Let x be the amount of money Ann has. Write an algebraic expression for each of the following

a) Macro has \$6 less than Ann has

b) Olivio has 3 times as much money as Ann.

c)   Franchesca has \$5 more than Ann.

Solution :

a) Here amount that Macro and Ann are having being compared.

Here we see the phrase less than, so we have to use subtraction sign.

Macro has = x - 6

b) 3 times = 3 multiplied by

Olivio has = 3x

c) More than = +

Franchesca has = 5 + x

Problem 2 :

The product of 9 and a number yields 45. Find the number.

A) 6    B) 36     C) 5     D) 405

Solution :

Writing variable equation :

Let x be the unknown number.

The product of 9 and a number = 9x

9x = 45

Solving for x :

To isolate x, we divide by 9 on both sides.

x = 45/9

x = 5

Problem 3 :

The sum of 2, 6, and a number amounts to 15. Find the number.

A) 7    B) 23    C) 19     D) 11

Solution :

Creating variable equation :

Let x be the unknown number.

The sum of 2, 6 and a number = 15

2 + 6 + x = 15

Solving for x :

8 + x = 15

Subtracting by 8 on both sides.

x = 15 - 8

x = 7

So, the required number is 7.

Problem 4 :

The product of a number and -8 gives eight times the sum of that number and 36. Find the number.

A) -18    B) -8      C) 8      D) 18

Solution :

Creating verbal equation :

Let x be the unknown number.

The product of a number and -8 = -8x

eight times the sum of that number and 36 = 8(x + 36)

-8x = 8(x + 36)

Solving for unknown :

Dividing by 8 on both sides.

-x = x + 36

-x - x = 36

-2x = 36

Dividing by -2

x = 36/(-2)

x = -18

Write the sentence as an equation. Use x to represent "a number."

Problem 5 :

Seven subtracted from twice a number gives 17.

A) 2x - 7 = 17       B) 2(x - 7) = 17

C) 7 - 2x = 17          D) 7(2 - x) = 17

Solution :

Creating verbal equation :

Let x be the number.

Twice a number can be represented as 2x

7 subtracted from twice a number, then 2x - 7

So, option A is correct.

Problem 6 :

A number added to -19 is equal to -21.

A) x - 21 = -19    B) -19 + x = -21

C) x = -19 + 21     D) -19 - 21 = x

Solution :

Let x be the unknown number.

x is added to -19, then x + (-19)

That gives -21, then x + (-19) = -21

x - 19 = -21 or (-19) + x = -21

So, option B is correct.

Problem 7 :

Ten subtracted from a number yields 15.

A) 10 + x = 15          B) 10 - x = 15

C) x - 10 = 15           D) 15 - 10 = x

Solution :

Let x be the number.

10 subtracted from a number, then x - 10

That yields = 15, then x - 10 = 15

So, option C is correct.

Problem 8 :

The quotient of 24 and a number is 4.

A) x/24 = 4       B) 24 - x = 4       C) 24/x = 4

D) 24 x = 4

Solution :

Let x be the number.

While dividing 24 and number, we get 4.

24/x = 4, then option C is correct.

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