1. Lesson 3.4 Writing Two-Step Equations  Objective: You will solve problems by writing two-step equations so you can find additional quantities, as in Example 1.

2. Standardized Test Practice EXAMPLE 1

3. SOLUTION Standardized Test Practice Write and solve a two-step equation to find the number of flamingos. Write a verbal model. Let n be the number of additional flamingos.

4. EXAMPLE 1 Standardized Test Practice 2370 = 395n + 1580 Write an algebraic model. 2370 – 1580 = 395n + 1580 – 1580 Subtract 1580 from each side. 790 = 395n Simplify. 790 395 395n 395 = Divide each side by 395. 2 = n Simplify.

5. EXAMPLE 1 ANSWER The zoo can buy 2 new flamingos next year. An equation for finding the number of flamingos is 2370 = 395n + 1580. The correct answer is B. Standardized Test Practice

6. GUIDED PRACTICE for Example 1 Feeding Costs 1. It costs a zoo $1150 this year to feed tortoises. Each new tortoise costs $575 to feed. A zoo’s budget for tortoise food next year is $2875. How many new tortoises can the zoo buy next year? SOLUTION Write and solve a two-step equation to find the number of tortoise. Write a verbal model. Let n be the number of new tortoises.

7. GUIDED PRACTICE for Example 1 Number of new tortoise Budget available = Cost each new tortoise to feed + Cost of existing tortoise + 2875=575n1150 Write an algebraic model. 1150 – – 575n1725 = 575 Subtract 1150 from each side. Simplify. Divide each side by 575. n = 3 Simplify. ANSWER The Zoo can buy 3 new tortoises next year

8. Writing and Solving a Two-Step Equation EXAMPLE 2 The sum of 4 times a number plus –6 is 14. What is the number? 4 times a number and –6 is 14. Write a verbal model. 4 n + (–6) = 14 Translate. 4n – 6 = 14 Write equation. 4n – 6 + 6 = 14 + 6 Add 6 to each side. 4n = 20 Simplify. 4n4n 4 = 20 4 Divide each side by 4. n = 5 Simplify. ANSWER The number is 5.

9. Writing and Solving a Two-Step Equation EXAMPLE 3 You want to find how many pages you need to read per week in order to finish several books in six weeks. The books have a total of 1244 pages. You have already read 500 pages. How many pages do you have to read per week? Reading

10. EXAMPLE 3 1244 = 6p + 500 Write an algebraic model. 1244 – 500 = 6p + 500 – 500 Subtract 500 from each side. 744 = 6p SOLUTION Let p be the number of pages to read per week. Simplify. Divide each side by 6 744 = 6p 66 124 = p Simplify. ANSWER You have to read 124 pages per week. Writing and Solving a Two-Step Equation

11. GUIDED PRACTICE for Examples 2 and 3 6 times a number and –9 is –3. Write a verbal model. 6 n + (– 9) = –3 Translate. 6n – 9 = –3 Write equation. 6n – 9 + 9 = –3 + 9 Add 9 to each side. 6n = 6 Simplify. 6n6n 6 = 6 6 Divide each side by 6. n = 1 Simplify. 2. The difference of six times a number and 9 is 23. What is the number? ANSWER The number is 1.

12. GUIDED PRACTICE SOLUTION Let p be the number of pages to read per week. Total pages = Weeks left Pages per weeksPages read + 1244 = 5p + 741 Write an algebraic model. 3. What If? Suppose in Example 3 that you have read 714 pages and have five weeks left. How many pages do you have to read per week? for Examples 2 and 3

13. GUIDED PRACTICE ANSWER You have to read 106 pages per week 530 = 5p Simplify. 5 530 5p 5 = Divide each side by 5 to undo multiplication. p = 106 Simplify. 1244 – 741 = 6p + 741 – 741 Subtract 741 from each side. for Examples 2 and 3