VERBAL PHRASE TO TWO STEP EXPRESSIONS OR EQUATIONS

Translate the verbal phrase to algebraic expressions.

Problem 1 :

Six less than twice a number x is four

Solution :

Problem 2 :

Four more than the product of 2 and a

Solution :

Problem 3 :

Nine times a number decreased by four

Solution :

Let the number be x.

Problem 4 :

Seven more than the quotient of a number and 2 is 10

Solution :

Let the number be x.

Problem 5 :

One less than the product of four and a number is 11.

Solution :

Let x be the required number.

Problem 6 :

Ten more than the quotient of a number and 3 is 12.

Solution :

Let x be the required number.

Problem 7 :

 The sum of 9 and the quotient of x and 7 is 11.

Solution :

Problem 8 :

The product of 8 and the difference of n and 3.

Solution :

Problem 9 :

1) Two less than the quotient of 15 and a number.

(15/x) - 2

2)  Five times the sum of six and some number.

Let x be some number.

5(x + 6)

3) The quotient of 7 and d decreased by 9.

d decreased by 9 :

d - 9

7/(d - 9)

4) Twice the difference of y and three

2(y - 3)

5) The difference of 9 and the quotient of s and –4

9 - s/(-4)

9 + (s/4)

6) The sum of 5 and product of 7 and x

5 + 7x

7) Three more than quotient of 5 and a 

3 + (5/a)

8) The product of 4 and the difference of x and 3

4(x - 3)

Problem 9 :

You start a new job. After w weeks, you have (10w + 120) dollars in your savings account and (45w + 25) dollars in your checking account. Write an expression that represents the total in both accounts.

Solution :

Amount you have in your savings = (10w + 120)

Amount you have in your checking account = 45w + 25

Total in both accounts = 10w + 120 + 45w + 25

= 10w + 45w + 120 + 25

= 55w + 145

Total amount in both accounts is 55w + 145.

Problem 10 :

While catching fire flies, you and a friend decide to have a competition. After m minutes, you have (3m + 13) fire flies and your friend has (4m + 6) fire flies.

a. Write an expression that represents the number of fire flies you and your friend caught together.

b. The competition ends after 5 minutes. Who has more fire flies?

Solution :

a)

Number of fire flies you have = 3m + 13

Number of fire flies you have your friend = 4m + 6

Total number of fire flies = 3m + 13 + 4m + 6

= 3m + 4m + 13 + 6

= 7m + 19

b) 

You have more fire flies.

Problem 11 :

A square wrestling mat has a perimeter of (12x − 32) feet. Write an expression that represents the side length of the mat (in feet).

Solution :

Perimter of square = (12x - 32) feet

Side length of square = Perimeter of square / 4

= (12x - 32)/4

= 12x/4 - 32/4

= (3x - 8) feet

Problem 12 :

A table is 6 feet long and 3 feet wide. You extend the table by inserting two identical table leaves. The longest side length of each rectangular leaf is 3 feet. The extended table is rectangular with an area of (18 + 6x) square feet.

a. Make a diagram of the table and leaves.

b. Write an expression that represents the length of the extended table. What does x represent?

Solution :

a)

b)

Area of table after extending = 18 + 6x

Length = 6 + x + x

= 6 + 2x

Width = 3

= (6 + 2x)3

Area = 18 + 6x

So, length of table is 6 + 2x.