TRANSLATING SENTENCE INTO EQUATIONS

Let  x represent  the number. Use mental math to solve the equation. 

Problem 1 :

The sum of a number and 10 is 15.

Solution :

Let x be the number.

x + 10 = 15

Subtract 10 on both sides.

x = 15 - 10

x = 5

Problem 2 :

28 decreased by a number is18.

Solution :

Let x be the number.

28 - x = 18

Subtract 28 on both sides.

-x = 18 - 28

-x = -10

x = 10

Problem 3 :

The product of a number and 25 is 100.

Solution :

Let x be the number.

x ∙ 25 = 100

Divide by 25 on both sides.

x = 100/25

x = 4

Problem 4 :

The quotient of 49 and a number is 7.

Solution :

Let x be the number.

49/x = 7

Multiply by x on both sides.

49 = 7x

Divide by 7 on both sides.

x = 49/7

x = 7

Problem 5 :

The area of the rectangle is less than or equal to 50 meters. Write an inequality for the area using the dimensions in the diagram.

Solution:

Let the width of rectangle is x meter.

Length is 3x meter.

Area of rectangle = Length × Width

= 3x ∙ x

Area = 3x²

As per the question,

3x² ≤ 50

Problem 6 :

The distance between your house and the amusement park s 110 miles. Your rate of travel is 55 miles per hour. Use the formula d = rt to write an equation. Use mental math to solve the equation for the time you spend traveling.

Solution :

Given,

Distance d = 110 miles

rate r = 55 miles per hour

Use the formula d = rt

time = d/r

t = 110/55

time = 2 hours

Problem 7 :

Translate into mathematical symbols “the difference of a number and 4 is 10”. Let n represent the number.

A)  n - 4 = 10    B)  4 - n = 10    C)  10 - 4 = n    D)  10 – n = 4

Solution :

Given, the difference of a number and 4 is 10.

That is,

n – 4 = 10

So, option (A) is correct.

Problem 8 :

MULTIPLE CHOICE   Which is the correct algebraic translation of “Howard’s hourly wage h is $2 greater them Marla’s hourly wage m?”

A)  h < m+2   B)  h = m+2   C)  m = h+2   D)  h > m+2

Solution :

Given, Howard’s hourly wage h is $2 greater them Marla’s hourly wage m.

That is,

 h > m+2

So, option (D) is correct.

Problem 9 :

Find the volume of a cube when each side x is 10 feet.

Solution :

We know, volume of a cube = (side x side x side)

Here, side = 10 feet

= 10x10x10

= 1000

Therefore, volume of a cube = 1000 feet³

Problem 10 :

The rectangle shown at the right has an area of 32 square units. Write an equation to find the width x.

Solution :

Given,

Area = 32 square units

Length = 8 and Width = x

Area of a Rectangle = length x width

Width = Area/length

x = 32/8

x = 4

So, width x = 4.