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.

Sum

More than

Increased

Greater than

Plus

Added to



Addition (+)

Difference

Less than

decreased

fewer than

minus

subtracted

less



Subtraction (-)



Product

times

of

Multiplication (x)

divided by

quotient

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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