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Math 7 Lesson: Solving Two-Step Equations And Word Problems Name_____________________________ Block________ Date_________________ REVIEW STEPS FOR SOLVING TWO-STEP EQUATIONS: 1. Separate equation sides with a down through the = sign, and 2. Label the variable side of the equation. 3. On the variable side, circle the term that does not have a variable with it. 4. Cancel out that term you circled, by doing its inverse operation (“undo” or “cancel out”). Remember to do that inverse operation on BOTH sides of the equation! 5. If the variable term is being multiplied by a number, then divide both sides of the equation by that number, and you are finished solving. If the variable term is being divided by a number, then multiply both sides of the equation by that number, and you are finished solving. REVIEW PRACTICE: a) 3x 17 13 d) 2 x 11 15 7 g) 25 2x 1 b) 5 x 20 7 e) 31 x 14 h) 2 x 11 15 7 c) x 5 12 f) 3 x 6 18 4 i) 19 x 7 4.4 Two-step word problems 1. CONSTRUCTION Nick is building a screen door. The height of the door is 1 ft more than twice its width. What is the width of the door if it is 7 feet high? Let w = Name: __________________ 2. GEOMETRY A rectangle has a width of 6 inches and a perimeter of 26 inches. What is the length of the rectangle? Let L = 3. HOME IMPROVEMENT Patty is making a patio in her backyard using paving stones. She buys 44 paving stones and a flowerpot worth $7 for a total of $73. How much did each paving stone cost? 4. SHOPPING While at the music store, Jack bought 5 CDs, all at the same price. The tax on his purchase was $6, and the total was $61. What was the price of each CD? 5. TAXI A taxi service charges you $1.50 plus $0.60 per minute for a trip to the airport. The distance to the airport is 10 miles, and the total charge is $13.50. How many minutes did the ride to the airport take? 6. FOOD At the market, Drew buys a bunch of bananas for $0.35 per pound and a frozen pizza for $4.99. The total for his purchase was $6.04, without tax. How many pounds of bananas did Drew buy? 7. SHARING Aliyah had some candy to share. She first took ten pieces for herself and then evenly divided the rest among her four cousins. Each cousin received two pieces. With how many pieces did she start? 8. AGE How old am I if 400 reduced by 2 times my age is 244? 9. BUY AND SELL Jill sold half of her comic books and then bought sixteen more. She now has 36. With how many did she begin? 10. TRANSPORTATION For a field trip, 4 students can ride in cars and the rest must be divided evenly to ride in nine buses. How many students were in each bus if 472 students were on the trip? 11. HATS On Tuesday Andres bought five 12. FUNDRAISING The SHMS Orchestra was selling donuts as a fundraiser. Billy Jean sold fourteen dozen donuts for $70. How much did each dozen cost? How many donuts total did she sell? baseball caps. On Wednesday he gave half of all his hats away as gifts to friends. On Thursday there were only 17 left. How many did he have on Monday? Write and solve an equation for each problem. HOMEWORK 4.4 1. Eleven less than 5 times a number is 24. Find the number. 2. The quotient of a number and -9, increased by 10, is 11. Find the number. 3. Three more than 8 times a number is -29. Find the number. 4. The Nile River is 6690 kilometers long. This is 394 kilometers longer than the Amazon River. How long is the Amazon River? 5. The Empire State Building is 1250 feet tall. This is 140 feet more than twice the height of the Washington Monument. How tall is the Washington Monument? 6. A medium apple has 72 calories. This is ¾ of the calories in a medium banana. How many calories does a medium banana have? 7. The width of a singles tennis court is 27 feet. This is 1 foot more than 3 of the length. What is the length of the court? 1