### Prealgebra: Solving Equations

```Name: ____________________________________________ Prealgebra: Solving Equations
Topic D5: Applications | VERSION B Write the following phrases in symbols using the variable x. 1.
2.
3.
4.
The sum of twice x and 9 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 4 is 7. Find the number. 8.
The sum of a number and 2 is 6. Find the number. 9.
When 5 is subtracted from four times a number, the result is 3. Find the number. Seven x decreased by 4 Three times the sum of five x and 4 The sum of twice x and 4 10. When 8 is subtracted from three times a number, the result is 4. Find the number. 5.
Six x decreased by 3 11. Five times the sum of four times a number and 7 is β5. Find the number. 6.
Five times the sum of four x and 2 12. Four times the sum of three times a number and 4 is β8. Find the number. www.varsitylearning.com 1 Name: ____________________________________________ Prealgebra: Solving Equations
Topic D5: Applications | VERSION B 13. The length of a rectangle is twice its width. The perimeter is 12 meters. Find the length and the width. The length is m and the width is m. 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 °. !
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. 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. 18. A car rental company charges \$12 a day and 13 cents per mile for their cars. If a car were rented for 1 day for a total charge of \$38.91, how many miles was it driven? They drove miles. 19. Ryan has \$1.95 in dimes and nickels. If he has 6 more dimes than nickels, how many of each coin does he have? He has nickels and dimes. 20. Wages. Stephanie works in the publicity office at the state university. She is paid \$18 an hour for the first 35 hours she works each week and \$27 an hour for every hour after that. If she makes \$792 one week, how many hours did she work? She worked for hours. www.varsitylearning.com 2 Name: ____________________________________________ Prealgebra: Solving Equations
Topic D5: Applications | VERSION B Write the following phrases in symbols using the variable x. 1.
2.
3.
4.
The sum of twice x and 9 2π₯ + 9 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 4 is 7. Find the number. π + 4 = 7, π = 3 8.
The sum of a number and 2 is 6. Find the number. π + 2 = 6, π = 4 9.
When 5 is subtracted from four times a number, the result is 3. Find the number. 4π β 5 = 3, π = 2 Seven x decreased by 4 7π₯ β 4 Three times the sum of five x and 4 3(5π₯ + 4) The sum of twice x and 4 2π₯ + 4 10. When 8 is subtracted from three times a number, the result is 4. Find the number. 3π β 8 = 4, π = 4 5.
Six x decreased by 3 6π₯ β 3 11. Five times the sum of four times a number and 7 is β5. Find the number. 5 4π + 7 = β5, π = β2 6.
Five times the sum of four x and 2 5(4π₯ + 2) 12. Four times the sum of three times a number and 4 is β8. Find the number. 4 3π + 4 = β8, π = β2 www.varsitylearning.com 3 Name: ____________________________________________ Prealgebra: Solving Equations
Topic D5: Applications | VERSION B 13. The length of a rectangle is twice its width. The perimeter is 12 meters. Find the length and the width. The length is 4 m and the width is 2 m. 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 °. !
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. 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. 18. A car rental company charges \$12 a day and 13 cents per mile for their cars. If a car were rented for 1 day for a total charge of \$38.91, how many miles was it driven? They drove 207 miles. 19. Ryan has \$1.95 in dimes and nickels. If he has 6 more dimes than nickels, how many of each coin does he have? He has 9 nickels and 15 dimes. 20. Wages. Stephanie works in the publicity office at the state university. She is paid \$18 an hour for the first 35 hours she works each week and \$27 an hour for every hour after that. If she makes \$792 one week, how many hours did she work? She worked for 41 hours. www.varsitylearning.com 4 ```