TRANSLATE THE SENTENCES TO EQUATION INVOLVING DECIMALS

To translate the sentences to equation, we have to know about what are phrases we use to translate it into mathematical symbol.

To solve equations, we should know about inverse operations.

• Inverse operation of addition is subtraction.
• Inverse operation of subtraction is addition.
• Inverse operation of multiplication is division.
• Inverse operation of division is multiplication.

In the following exercises, translate and solve.

Problem 1 :

The difference of n and 1.9 is 3.4.

Solution :

n – 1.9 = 3.4

n = 3.4 + 1.9

n = 5.3

Problem 2 :

The difference of n and 1.5 is 0.8.

Solution :

n – 1.5 = 0.8

n = 0.8 + 1.5

n = 2.3

Problem 3 :

The product of -6.2 and x is -4.96.

Solution :

-6.2 x = - 4.96

x = -4.96 / -6.2

x = 0.8

Problem 4 :

The product of -4.6 and x is -3.22.

Solution :

-4.6 x = - 3.22

x = -3.22 / -4.6

x = 0.7

Problem 5 :

The quotient of y and -1.7 is -5.

Solution :

y / -1.7 = -5

y = (-5) (-1.7)

y = 8.5

Problem 6 :

The quotient of z and -3.6 is 3.

Solution :

z / -3.6 = 3

z = 3 (-3.6)

z = - 10.8

Problem 7 :

The sum of n and -7.3 is 2.4.

Solution :

n + (-7.3) = 2.4

n – 7.3 = 2.4

n = 2.4 + 7.3

n = 9.7

Problem 8 :

The sum of n and -5.1 is 3.8.

Solution :

n + (-5.1) = 3.8

n – 5.1 = 3.8

n = 3.8 + 5.1

n = 8.9

Problem 9 :

You clean a community park for 6.5 hours. You earn $42.25. How much do you earn per hour?

Solution :

Number of hours worlksing =- 6.5 hours

Amount he earns = 42.25

Amount he earns per hour = 42.25/6.5

= 6.5

So, $ 6.5 is amount he earns per hour.

Problem 10 :

A rocket is scheduled to launch from a command center in 3.75 hours. What time is it now?

Solution :

Launch time is at 11 : 20 am

Let t be the required time

In 3.75 hours, to convert 0.75 hours to minutes we have to multiply by 60.

= 0.75 x 60

= 45 minutes

t + 3 : 45 = 11 : 20

t = 11 : 20 - 3 : 45

= 11 hours 20 minutes - 3 hours 45 minutes

Since we cannot subtract 45 minutes from 20 minutes, we borrow minutes from 11 hours.

= (10 - 3) hours (80 - 45) minutes

= 7 hours 35 minutes

= 7 : 35

Problem 11 :

Without solving, determine whether the solution of −2x = −15 is greater than or less than −15. Explain.

Solution :

-2x = -15

x = 15/2

Since we have negative on both sides, we cancel the negative signs. The value of x will be positive. Every positive number will be greater than the negative number.

Problem 12 :

Some ant species can carry 50 times their body weight. It takes 32 ants to carry the cherry. About how much does each ant weigh?

Solution :

Weight of a cherry = 4800 mg

Let w be the weight of an ant.

Each ant can carry the weight which is 50w.

Number of ants involved here = 32

32(50w) = 4800

w = 4800 / (32 x 50)

w = 3

So, weight of each ant is 3 mg.

Problem 13 :

One-fourth of the girls and one-eighth of the boys in a class retake their school pictures. The photographer retakes pictures for 16 girls and 7 boys. How many students are in the class?

Solution :

Number of girls retaking the picture = 16 girls

Number of boys retaking the picture = 7 boys

Let g be the total number of girls and b be total number of boys.

1/4 of g = 16

(1/4) x g = 16

g = 16(4)

g = 64

1/8 of b = 7

1/8 x b = 7

b = 7(8)

b = 56

Total number of students = number of girls + number of boys

= 64 + 56

= 120 students

Problem 14 :

The height (in feet) of a tree after x years is 1.5x + 15. After how many years is the tree 24 feet tall?

Solution :

1.5 x + 15 = 24

1.5x = 24 - 15

1.5x = 9

x = 9/1.5

x = 3/0.5

x = 6

So, after 6 years the tree will be the height of 24 feet.

Problem 15 :

Use the table to find the number of miles x you need to run on Friday so that the mean number of miles run per day is 1.5.

Solution :

Mean = sum of all quantities / total number of items

(2 + 0 + 1.5 + 0 + x)/5 = 1.5

(3.5 + x)/5 = 1.5

3.5 + x = 1.5(5)

3.5 + x = 7.5

x = 7.5 - 3.5

x = 4

So, you need to run 4 miles on Friday.