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Equations with Decimals Worksheet

Equations with Decimals Worksheet
  • Page 1
 1.  
Jimmy and Arthur bought a vanilla cake on Francis's birthday, which cost $4.40. Both of them shared the cost equally. Find the share of each person.
a.
$4.20
b.
$1.60
c.
$3.20
d.
$2.20


Solution:

Let x be the share of each person.

2x = 4.40
[Write the equation from data.]

x = 4.402
[Divide each side by 2.]

x = 2.20
[Simplify.]

The share of each person is $2.20.


Correct answer : (4)
 2.  
Solve -6x + 8 = 18 and round the value of x to the nearest hundredth.
a.
1.67
b.
-1.67
c.
-0.67
d.
0.67


Solution:

-6x + 8 = 18
[Original equation.]

-6x = 10
[Subtract 8 from each side.]

x = 10-6
[Divide each side by -6.]

x = -1.666
[Simplify.]

x -1.67
If the digit in the thousandth place is greater than or equal to 5, round up. Otherwise round down.
[Round to the nearest hundredths.]


Correct answer : (2)
 3.  
Solve 21.3x + 14.3 = 55.2 and round the value of x to the nearest tenth.
a.
2.1
b.
1.8
c.
2.0
d.
1.9


Solution:

21.3x + 14.3 = 55.2
[Original equation.]

21.3x = 40.9
[Subtract 14.3 from each side.]

x = 40.921.3
[Divide each side by 21.3.]

x = 1.920
[Simplify.]

x » 1.9
[Rounded to the nearest tenth.]


Correct answer : (4)
 4.  
A 21-storied building was rented to 21 different software companies for $23668 as a whole, per month. Find the amount of rent paid by each company, if each company pays the same rent.
a.
$1127.05
b.
$1125.05
c.
$1126.05
d.
$1128.05


Solution:

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

21x = 23668
[Write an equation.]

x = 2366821
[Divide each side by 21.]

x = 1127.0476
[Simplify.]

x » 1127.05
[Round to nearest cent.]

So, the rent paid by each company is $1127.05.


Correct answer : (1)
 5.  
Mrs. Ursula took a face-lifting treatment that costed her $784.35. The total cost included the cost of the treatment and a 8% tax. Find the cost of the treatment without the tax.
a.
$726.25
b.
$706.25
c.
$746.25
d.
$716.25


Solution:

Let c be the cost of the face-lifting treatment without the tax.

The equation to be solved to find the cost of the treatment without the tax is Cost of the treatment without tax + Tax x (Cost of the treatment without tax) = Total cost.

c + 0.08 x c = 784.35
[Original equation.]

1.08c = 784.35
[Combine like terms.]

c = 784.351.08
[Divide each side by 1.08.]

= 726.25
[Simplify.]

So, the cost of the face-lifting treatment without the tax is $726.25.


Correct answer : (1)
 6.  
Negative twenty-two hundredths times a number x equals the opposite of eighty-eight and eight tenths. Find the value of x. a A
a.
4.0363
b.
40.363
c.
403.63
d.
430.63


Solution:

Negative twenty-two hundredths times a number x = -0.22x.

The opposite of eighty-eight and eight tenths = -88.8.

-0.22x = -88.8
[Original equation.]

x = -88.8-0.22
[Divide each side by -0.22.]

x = 403.63
[Simplify.]

So, the value of x is 403.63


Correct answer : (3)
 7.  
The sum of the opposite of twelve hundredths times a number x and thirteen hundredths equals fifteen hundredths. Solve for x.
a.
-0.166
b.
-0.0166
c.
0.166
d.
0.0166


Solution:

The opposite of twelve hundredths times a number x = -0.12x.

The sum of the opposite of twelve hundredths times a number x and thirteen hundredths is -0.12x + 0.13

Fifteen hundredths = 0.15

-0.12x + 0.13 = 0.15
[Write the equation.]

-0.12x = 0.02
[Subtract 0.13 from each side.]

x = 0.02-0.12
[Divide each side by -0.12]

x = -0.166
[Simplify.]


Correct answer : (1)
 8.  
5 participants ran in a 941 meters relay with each covering the same distance. How much distance did each cover?
a.
187.20 meters
b.
189.20 meters
c.
186.20 meters
d.
188.20 meters


Solution:

Let x be the distance covered by each of them.

5x = 941
[Original equation.]

= 9415
[Divide each side by 5.]

= 188.20
[Simplify.]

Each of them covers a distance of 188.20 meters.


Correct answer : (4)
 9.  
Rose wants to buy a bouquet of daisies and tulips for $10.5. A bunch of daisies cost $6 and the tulips cost $1.5 each. Solve the equation 1.5t + 6 = 10.5 to find t, the number of tulips Rose can buy.
a.
4
b.
5
c.
3
d.
2


Solution:

1.5t + 6 = 10.5
[Original equation.]

1.5t = 4.5
[Subtract 6 from each side.]

t = 4.51.5
[Divide each side by 1.5]

t = 3
[Simplify.]

Rose can buy 3 tulips.


Correct answer : (3)
 10.  
Mike arranged for a dinner at a restaurant on the occasion of his birthday. The total bill was $895.75, which included the cost of the dinner and a 9% tip. Find the cost of the dinner arranged by Mike without the tip.
a.
$811.79
b.
$821.79
c.
$831.79
d.
None of the above


Solution:

Let c be the cost of the dinner without the tip.

The equation to be solved to find the cost of the dinner without the tip is, Cost of the dinner without tip + Tip × (Cost of the dinner without tip ) = Total bill.

c + 0.09 × c = 895.75
[Original equation.]

1.09c = 895.75
[Combine like terms.]

c = 895.751.09
[Divide each side by 1.09.]

c = 821.788
[Simplify.]

c 821.79
[Round to the nearest cent.]

The cost of the dinner without the tip is $821.79.


Correct answer : (2)

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