TRANSLATING PHRASE INTO EQUATIONS AND INEQUALITIES

To translate phrase into equation or inequality, we have to be aware of the following terms.

+ Sum, more, plus x Times, multiplied, product

- Difference, less, subtracted / Divided by, quotient

Write the sentence as an equation or an inequality. Let x represent  the number.

Problem 1 :

The sum of 20 and a number is 30.

Solution :

Let x be the number.

As per the question,

x + 20 = 30

Hence, the equation is x + 20 = 30.

Problem 2 :

A number increased by 10 is greater than or equal to 44.

Solution :

Let x be the number.

As per the question,

x + 10 ≥ 44

Hence, the inequality is x + 10 ≥ 44.

Problem 3 :

18 decreased by a number is 6.

Solution :

Let x be the number.

As per the question,

x - 18 = 6

Hence, the equation is x - 18 = 6.

Problem 4 :

35 is less than the difference of 21 and a number.

Solution :

Let x be the number.

As per the question,

35 < x - 21

Hence, the inequality is 35 < x - 21.

Problem 5 :

The product of 13 and a number is greater than 60.

Solution :

Let x be the number.

As per the question,

13x > 60

Hence, the inequality is 13x > 60.

Problem 6 :

7 times a number is 56.

Solution :

Let x be the number.

As per the question,

7x = 56

Hence, the equation is 7x = 56.

Problem 7 :

A number divided by 22 is less than 3.

Solution :

As per the question,

x/22 < 3

Hence, the inequality is x/22 < 3.

Problem 8 :

The quotient of 35 and a number is 7.

Solution :

As per the question,

35/x = 7

Hence, the equation is 35/x = 7.

Problem 9 :

A number x divided by 9 is less than 17.

Solution :

As per the question,

x/9 < 17

Hence, the inequality is x/9 < 17.

Problem 10 :

The product of 10 and a number x is 50.

Solution :

As per the question,

10x = 50

Hence, the equation is 10x = 50.

Problem 11 :

A number y plus 10 is greater than or equal to 57.

Solution :

As per the question,

y+10 ≥ 57

Hence, the inequality is y+10 ≥ 57.

Problem 12 :

A number y minus 6 is 15.

Solution :

As per the question,

y - 6 = 15

Hence, the equation is y - 6 = 15.

Problem 13 :

Ten servers decorate 25 tables for a wedding. Each table is decorated as shown. Let c be the total number of white and purple candles. Which equation can you use to find c ?

a) c = 25 + (4 × 6)       b) c = 25(4 + 6)      c) c = 10(25 + 4 + 6)    d)  c = 10(4 + 6)

Solution :

Total number of tables = 25

By looking at the decoration, we have 4 white candles and 6 purple candles.

Total number of candles in one table = 4 + 6

Number of candles in 25 tables = 25 (4 + 6)

So, option c is correct.

Problem 14 :

In a magic square, the sum of the numbers in each row, column, and diagonal is the same. Write and solve equations to find the values of a, b, and c.

Solution :

Sum of quantities in the first row,

a + 37 + 16 -------(1)

Sum of quantities in the third column

16 + b + 28 -------(2)

Sum of quantities in the third row,

34 + c + 28 -------(3)

Sum of quantitties in diaognal,

= 35 + 25 + 16

= 76 -------(4)

Problem 15 :

You are fishing and are allowed to catch at most 3 striped bass. Each striped bass must be no less than 18 inches long.

a. Write and graph an inequality to represent the number of striped bass you are allowed to catch.

b. Write and graph an inequality to represent the length of each striped bass you are allowed to catch.

Solution :

a) Maximum number of striped bass we are allowed to catch is x.

x ≤ 3

b) Length of each striped bass = 18 (maximum)

x ≤ 18

Problem 16 :

• A bus ride costs $1.50.
• A 30-day bus pass costs $36.

Write an inequality to represent the number of bus rides you would need to take for the bus pass to be a better deal.

Solution :

Let x be the number of bus rides

1.50x > 36

x > 36/1.5

x > 24

So, if you are going to take more than 24 bus rides in 30 days, then buying the 30-day bus pass would be a better deal.

Problem 17 :

Fifty people are seated in a movie theater. The maximum capacity of the theater is 425 people. Write an inequality to represent the number of additional people who can still be seated.

Solution :

Let x be the number of additional people who can still be seated.

Number of people are seated in a theater.

x + 50 ≤ 425

x ≤ 425 - 50

x ≤ 375