Name: ____________________________________________ Prealgebra: Solving Equations
Topic D5: Applications | VERSION A Write the following phrases in symbols using the variable x. 1.
2.
3.
4.
The sum of twice x and 4 Use the six steps in the "Blueprint for Problem Solving" to solve the following word problem. You may recognize the solution by just reading the problem. Use n as the variable for the number and write the equation used to describe the problem. 7.
The sum of a number and 3 is 6. Find the number. 8.
The sum of a number and 4 is 16. Find the number. 9.
When 5 is subtracted from three times a number, the result is 4. Find the number. The sum of four x and 3 Six x decreased by 9 Twelve x decreased by 2 10. When 9 is subtracted from three times a number, the result is 3. Find the number. 5.
Three times the sum of four x and 8 6.
Two times the sum of six x and negative 3 11. Five times the sum of three times a number and 4 is -­‐10. Find the number. 12. Three times the sum of four times a number and 4 is -­‐12. Find the number. www.varsitylearning.com 1 Name: ____________________________________________ Prealgebra: Solving Equations
Topic D5: Applications | VERSION A 13. The length of a rectangle is twice its width. The perimeter is 30 meters. Find the length and the width. The length is m and the width is m. 17. Diane is 23 years older than her daughter Amy. In 5 years, the sum of their ages will be 91. How old are they now? Amy is years old, and Diane is years old. 14. Two angles in a triangle are equal, and their sum is equal to the third angle in the triangle. What are the measures of each of the three interior angles? The measures of the two equal angles are °, °, and the third angle is °. 18. A car rental company charges $13 a day and 17 cents per mile for their cars. If a car were rented for 1 day for a total charge of $27.79, how many miles was it driven? They drove miles. !
15. The smallest angle in a triangle is as large as the !
largest angle. The third angle is twice the smallest angle. Find the three angles. The measures of the angles from smallest to biggest are °, °, and °. 16. Pat is 20 years older than his son Patrick. In 2 years, the sum of their ages will be 90. How old are they now? Patrick is years old, and Pat is years old. 19. Lucas has $1.35 in dimes and nickels. If he has 12 more nickels than dimes, how many of each coin does he have? He has nickels and dimes. 20. Wages. JoAnn works in the publicity office at the state university. She is paid $10 an hour for the first 35 hours she works each week and $15 an hour for every hour after that. If she makes $560 one week, how many hours did she work? She worked for hours. www.varsitylearning.com 2 Name: ____________________________________________ Prealgebra: Solving Equations
Topic D5: Applications | VERSION A Write the following phrases in symbols using the variable x. 1.
2.
3.
4.
The sum of twice x and 4 2𝑥 + 4 Use the six steps in the "Blueprint for Problem Solving" to solve the following word problem. You may recognize the solution by just reading the problem. Use n as the variable for the number and write the equation used to describe the problem. 7.
The sum of a number and 3 is 6. Find the number. 𝑛 + 3 = 6, 𝑛 = 3 8.
The sum of a number and 4 is 16. Find the number. 𝑛 + 4 = 16, 𝑛 = 12 9.
When 5 is subtracted from three times a number, the result is 4. Find the number. 3𝑛 − 5 = 4, 𝑛 = 3 The sum of four x and 3 4𝑥 + 3 Six x decreased by 9 6𝑥 − 9 Twelve x decreased by 2 12𝑥 − 2 10. When 9 is subtracted from three times a number, the result is 3. Find the number. 3𝑛 − 9 = 3, 𝑛 = 4 5.
Three times the sum of four x and 8 3(4𝑥 + 8) 6.
Two times the sum of six x and negative 3 2(6𝑥 + (−3)) 11. Five times the sum of three times a number and 4 is -­‐10. Find the number. 5 3𝑛 + 4 = −10, 𝑛 = −2 12. Three times the sum of four times a number and 4 is -­‐12. Find the number. 3 4𝑛 + 4 = −12, 𝑛 = −2 www.varsitylearning.com 3 Name: ____________________________________________ Prealgebra: Solving Equations
Topic D5: Applications | VERSION A 13. The length of a rectangle is twice its width. The perimeter is 30 meters. Find the length and the width. The length is 10 m and the width is 5 m. 17. Diane is 23 years older than her daughter Amy. In 5 years, the sum of their ages will be 91. How old are they now? Amy is 29 years old, and Diane is 52 years old. 14. Two angles in a triangle are equal, and their sum is equal to the third angle in the triangle. What are the measures of each of the three interior angles? The measures of the two equal angles are 45 °, 45 °, and the third angle is 90 °. 18. A car rental company charges $13 a day and 17 cents per mile for their cars. If a car were rented for 1 day for a total charge of $27.79, how many miles was it driven? They drove 87 miles. !
15. The smallest angle in a triangle is as large as the !
largest angle. The third angle is twice the smallest angle. Find the three angles. The measures of the angles from smallest to biggest are 30 °, 60 °, and 90 °. 16. Pat is 20 years older than his son Patrick. In 2 years, the sum of their ages will be 90. How old are they now? Patrick is 33 years old, and Pat is 53 years old. 19. Lucas has $1.35 in dimes and nickels. If he has 12 more nickels than dimes, how many of each coin does he have? He has 17 nickels and 5 dimes. 20. Wages. JoAnn works in the publicity office at the state university. She is paid $10 an hour for the first 35 hours she works each week and $15 an hour for every hour after that. If she makes $560 one week, how many hours did she work? She worked for 49 hours. www.varsitylearning.com 4