1. Meaning of Equations and Inequalities

2.  Today’s standard: CCSS.MATH.CONTENT.7.EE.B.4  Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.  Students should answer at least 75% of questions correctly on an exit ticket.

3.  Being able to solve equations and inequalities is meaningless unless we understand what the answer represents. Knowing “x = 5” is not useful but knowing “There are 5 apples” or “It takes 5 hours to earn a certain amount of money” is useful.  Today, we will work with word problems and not only come up with a numerical answer but also state what it means.

4. Bob has $300 in his bank account and adds $25 more each month. This situation can be represented by the equation 300 + 25m = A What do m and A represent in this equation? m = number of months A = amount of money in Bob’s bank account

5. From last slide: 300 + 25m = A Solve 300 + 25m = 700 -300 -300 25m = 400 ÷25 ÷25 m = 16 Write in a complete sentence what your answer means. Hint: look back at what each variable represents. In 16 months Bob will have $700 in his bank account. (Here, A was replaced by 700, so the bank account must be $700. We found m was 16 so there were 16 months).

6. The temperature is -40°. Every hour the temperature rises by 8°. t = 8h – 40 What do t and h represent in this equation? t = temperature h = # of hours I want the temperature to be 16°. Use the equation to solve for h. 16 = 8h – 40 +40 + 40 56 = 8h ÷8 ÷8 7 = h Write a complete sentence explaining what your answer means. In 7 hours the temperature will be 16°.

7. A taxi charges a $10 entry fee and $2 per mile driven. Write an equation for this situation using two variables of your choice. State what each variable stands for. c = 2m + 10 c = total cost m = # of miles Use your equation to find the cost of a 17 mile trip. c = 2(17) + 10 c = 34 + 10 c = 44

8.  Bob wants to buy a $37 game. He has $9 and earns $5 more for each newspaper route.  Write an inequality that describes this situation. State what your variable stands for.  9 + 5r > 37 r = # of newspaper routes  Solve the inequality  9 + 5r > 37 -9 -9 5r > 28 ÷5 ÷5 r > 5.6  Explain in a sentence what your answer states.  Bob must do at least 6 newspaper routes to be able to afford the game.

9.  Amy can spend up to $20 at the store. She needs to buy a $4.50 loaf of bread and then as much $0.50 candy as she wants.  Write an inequality for this situation and state what your variable stands for. Then solve it.  0.50c + 4.50 < 20.00 c = # of candy  -4.50 -4.50 0.50c < 15.50 ÷0.50 ÷0.50 c < 31  Explain in a sentence what your answer means.  Amy can buy up to 31 pieces of candy.