(For help, go to Lesson 1-1.) ALGEBRA 1 LESSON 2-7 Write a variable expression for each situation. 1.value in cents of q quarters 2.twice the length 3.number of miles traveled at 34 mi/h in h hours 4.weight of 5 crates if each crate weighs x kilograms 5.cost of n items at $3.99 per item Equations and Problem Solving 2-7

Solutions 1.value in cents of q quarters: 25q 2.twice the length : 2 3.number of miles traveled at 34 mi/h in h hours: 34h 4.weight of 5 crates if each crate weighs x kilograms: 5x 5.cost of n items at $3.99 per item: 3.99n Equations and Problem Solving ALGEBRA 1 LESSON

The sum of three consecutive integers is 72. Find the integers. Relate: first plus second plus third is 72 integer integer integer Define: Let x = the first integer. Then x + 1 = the second integer, and x + 2 = the third integer. Write: x + x x + 2 = 72 Equations and Problem Solving ALGEBRA 1 LESSON

If x = 23, then x + 1 = 24, and x + 2 = 25. The three integers are 23, 24, and 25. x + x x + 2 = 72 3x + 3 = 72Combine like terms. 3x + 3 – 3 = 72 – 3Subtract 3 from each side. 3x = 69Simplify. Equations and Problem Solving ALGEBRA 1 LESSON (continued) = Divide each side by 3. 3x33x x = 23Simplify.

1.The sum of three consecutive integers is 117. Find the integers. 2.You and your brother started biking at noon from places that are 52 mi apart. You rode toward each other and met at 2:00 p.m. Your brother’s average speed was 4 mi/h faster than your average speed. Find both speeds. 3.Joan ran from her home to the lake at 8 mi/h. She ran back home at 6 mi/h. Her total running time was 32 minutes. How much time did it take Joan to run from her home to the lake? 38, 39, 40 your speed: 11 mi/h; brother’s speed: 15 mi/h about 13.7 minutes Equations and Problem Solving ALGEBRA 1 LESSON