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Write an Equation

Write an Equation. COURSE 2 LESSON 2-7. (For help, go to Lesson 2-3.). Write and solve an equation for each sentence. 1. Seven fewer than a number is 12. 2. The sum of 9 and a number is equal to 36. 3. Twenty-seven is 10 less than a number. 4. Seventeen more than a number is 5. 2-7.

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Write an Equation

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  1. Write an Equation COURSE 2 LESSON 2-7 (For help, go to Lesson 2-3.) Write and solve an equation for each sentence. 1. Seven fewer than a number is 12. 2. The sum of 9 and a number is equal to 36. 3. Twenty-seven is 10 less than a number. 4. Seventeen more than a number is 5. 2-7

  2. Write an Equation COURSE 2 LESSON 2-7 Solutions 1.n – 7 = 12 2. 9 + n = 36 n – 7 + 7 = 12 + 7 9 – 9 + n = 36 – 9 n = 19 n = 27 3. 27 = n – 10; n = 27 + 10 = 37 4.n + 17 = 5; n = 5 – 17 = –12 2-7

  3. 36 of the 64 students going to the science fair will ride in a bus. The rest of the students will ride in vans that can carry 6 students each. You need to find the number of vans that are needed. There are two groups of students going to the science fair: those riding in a bus, and those riding in vans. The sum of the two groups cannot be less than the total number of students. Write an equation and solve the problem. Write an Equation COURSE 2 LESSON 2-7 Of the 64 students going to the science fair, 36 will ride in a bus. The others will ride in vans that each carry 6 students. How many vans are needed? 2-7

  4. Words students plus students times number equals total • in the in each of vans students • bus van • Let v = the number of vans needed. • Equation 36 + 6 • v = 64 36 + 6v = 64 Solve the equation. 36 – 36 + 6v = 64 – 36 Subtract 36 from each side. 6v = 28 or v = 4.6 Simplify. Since you cannot have 4.6 vans, 5 vans are needed. Write an Equation COURSE 2 LESSON 2-7 (continued) 2-7

  5. Each van will carry 6 students. The total number of students able to ride in the vans and the bus is 36 + 5 • 6, or 66 students. If 4 vans are used, the total is 36 + 4 • 6, or 60 students. Since this is less than the total students traveling, the answer checks. Write an Equation COURSE 2 LESSON 2-7 (continued) 2-7

  6. Think about the information and what you are being asked to find. Lindsey has $12, and this is $3 more than twice the cost of a movie. You are asked to find the cost of a movie. Since you are given the relationship between the numbers, an equation can help you solve the problem. Write an Equation COURSE 2 LESSON 2-7 Lindsey has saved $12 to go to the movies. This is $3 more than twice the cost of a movie. What is the cost of a movie? 2-7

  7. Words two times cost of a plus three equals total amount • movie of money • Let c = the cost of a movie. • Equation 2 • c + 3 = 12 2c + 3 = 12 2c + 3 – 3 = 12 – 3Subtract 3 from each side. 2c = 9Simplify. 9 2 2c 2 = Divide each side by 2. c = 4.5 Simplify. Write an Equation COURSE 2 LESSON 2-7 (continued) The cost of a movie is $4.50. 2-7

  8. To check the solution, use 4.5 for the cost of a movie. Since 2 • 4.5 + 3 = 9 + 3 = 12, the answer is correct. Write an Equation COURSE 2 LESSON 2-7 (continued) 2-7

  9. Write an Equation COURSE 2 LESSON 2-7 Solve each problem by writing and solving an equation. 1. Ravi bought 3 identical shirts and paid a sales tax of $2.84. The total cost was $50.18. What was the cost of each shirt? 2. In 1976, Jimmy Carter received 58 fewer electoral votes than 5 times the number received by John Adams in 1796. Carter received 297 electoral votes. How many did Adams receive? 3s + 2.84 = $50.18; $15.78 5h = 297 + 58; 71 votes 2-7

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