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.

2.
Solve -6$x$ + 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.]

3.
Solve 21.3$x$ + 14.3 = 55.2 and round the value of $x$ to the nearest tenth.
 a. 2.1 b. 1.8 c. 2 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.]

4.

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.

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

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.]

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.