﻿ Equations with Decimals Worksheet - Page 2 | Problems & Solutions
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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$1.25 for every patient she attends in a hospital. Solve the equation 8.75 + 1.25$p$ = 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 $13.75 in an hour. Correct answer : (3) 12. Solve: 3.6$x$ + 10.0 = 2.6$x$ - 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 -3$x$ - 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 -3$x$ - 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. 0.7$x$ = 13.5 b. 0.007$x$ = 13.5 c. 0.07$x$ = 1.35 d. 0.07$x$ = 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. -0.46$x$ = 57.6 b. 0.046$x$ = 57.6 c. 0.46$x$ = 57.6 d. -0.046$x$ = 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 55.5$x$ + 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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