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Equations with Decimals Worksheet - Page 2

Equations with Decimals Worksheet
  • Page 2
 11.  
Rose is paid $8.75 an hour and $1.25 for every patient she attends in a hospital. Solve the equation 8.75 + 1.25p = 13.75 to find out the number of patients she has to attend to earn $13.75 in an hour.
a.
6
b.
3
c.
4
d.
5


Solution:

Let p be the number of patients Rose has to attend to earn $13.75 in an hour.

8.75 + 1.25p = 13.75
[Original equation.]

1.25p = 5
[Subtract 8.75 from each side.]

p = 51.25
[Divide each side by 1.25.]

p = 4
[Simplify.]

Rose has to attend 4 patients in order to earn $13.75 in an hour.


Correct answer : (3)
 12.  
Solve: 3.6x + 10.0 = 2.6x - 4.0
a.
-15.1
b.
14
c.
-14
d.
15.1


Solution:

3.6x + 10.0 = 2.6x - 4.0
[Original equation.]

10(3.6x + 10.0) = 10(2.6x - 4.0)
[Multiply each side by 10 to rewrite the equation without decimals.]

36x + 100 = 26x - 40
[Use distributive property.]

10x + 100 = -40
[Subtract 26x from each side.]

10x = -140
[Subtract 100 from each side.]

x = -140 / 10
[Divide each side by 10.]

x = -14
[Simplify.]


Correct answer : (3)
 13.  
Solve -3x - 5 = 11 and round the value of x to the nearest hundredths.
a.
-5.33
b.
4.33
c.
-4.33
d.
5.33


Solution:

-3x - 5 = 11
[Original equation.]

-3x = 16
[Add 5 to each side.]

x = 16-3
[Divide each side by -3.]

x = -5.3333
[Simplify.]

x -5.33
[Round to the nearest hundredth.]

The nearest hundredth value of x is rounded to -5.33.


Correct answer : (1)
 14.  
Solve -3x - 5 = 11 and round the value of x to the nearest hundredths.
a.
-5.33
b.
4.33
c.
5.33
d.
-4.33


Solution:

-3x - 5 = 11
[Original equation.]

-3x = 16
[Add 5 to each side.]

x = 16-3
[Divide each side by -3.]

x = -5.3333
[Simplify.]

x -5.33
[Round to the nearest hundredth.]

To the nearest hundredths value of x is rounded to -5.33.


Correct answer : (1)
 15.  
The rent of an apartment is $819.24 per month in Milan. Ed, Bill, Brad and Victor plan to share the apartment. Find the share that each of them has to pay.
a.
$206.81
b.
$202.81
c.
$204.81
d.
$208.31


Solution:

Let x be the share of each of them.

4x = 819.24
[Original equation.]

x = 819.244
[Divide each side by 4.]

x = 204.81
[Simplify.]

The share that each of them has to pay is $204.81


Correct answer : (3)
 16.  
Write the equation for the sentence, 'Seven-hundredths times a number x equals thirteen and five tenths'.
a.
0.7x = 13.5
b.
0.007x = 13.5
c.
0.07x = 1.35
d.
0.07x = 13.5


Solution:

Seven-hundredths times a number x is 0.07x.

Thirteen and five tenths is 13.5

0.07x = 13.5
[Write the equation.]


Correct answer : (4)
 17.  
"The product of negative forty-six hundredths and a number x equals fifty-seven and six tenths." Which of the equations best represents the sentence?
a.
-0.46x = 57.6
b.
0.046x = 57.6
c.
0.46x = 57.6
d.
-0.046x = 57.6


Solution:

Forty-six hundredths is 0.46

The product of negative forty-six hundredths and a number x is -0.46x.

Fifty-seven and six tenths is 57.6

The equation will be -0.46x = 57.6


Correct answer : (1)
 18.  
"Seven-hundredths times a number x equals thirteen and five tenths and solve for x." Write an equation for the sentence.
a.
190.85
b.
19.85
c.
19.28
d.
192.85


Solution:

Seven-hundredths times a number x is 0.07x.

Thirteen and five tenths is 13.5

0.07x = 13.5
[Original equation.]

x = 13.50.07
[Divide each side by 0.07]

x = 192.85
[Simplify.]

The value of x is 192.85


Correct answer : (4)
 19.  
Solve 55.5x + 49.6 = 83.8 and round the value of x to the nearest tenth.
a.
0.8
b.
0.7
c.
0.6
d.
0.5


Solution:

55.5x + 49.6 = 83.8
[Original equation.]

55.5x = 34.2
[Subtract 49.6 from each side.]

x = 34.255.5
[Divide each side by 55.5.]

x = 0.616
[Simplify.]

x » 0.6
[Rounded to the nearest tenth.]


Correct answer : (3)
 20.  
A 16-storied building was rented to 16 different software companies for $13473 as a whole, per month. Find the amount of rent paid by each company, if each company pays the same amount of rent.
a.
$840.06
b.
$843.06
c.
$842.06
d.
$841.06


Solution:

Let x be the amount of rent paid by each company.

16x = 13473
[Write an equation.]

x = 1347316
[Divide each side by 16.]

x = 842.0625
[Simplify.]

x » 842.06
[Round to nearest cent.]

So, the amount of rent paid by each company is $842.06.


Correct answer : (3)

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