Report

Express each of the following rules as an equation. Use single letters to stand for the variables. Identify what each letter represents. 1. The area a of a rectangle is its length l multiplied by its width w. Equation: ___________________ a represents _______________ l represents _______________ w represents _______________ 2. The number of hot dogs n needed for the picnic is two for each student s. Equation: ___________________ n represents _______________ __ s represents _______________ Express each of the following rules as an equation. Use single letters to stand for the variables. Identify what each letter represents. 3. Taxi fare f is $2.00 plus $1.10 per mile m. Equation: ___________________ f represents _______________ m represents _______________ 4. An airplane is traveling at 550 miles per hour. Write an equation for the distance d the plan travels in h hours. Equation: ___________________ d represents _______________ h represents _______________ Express each of the following rules as an equation. Use single letters to stand for the variables. Identify what each letter represents. 5. Potatoes sell for $0.25 per pound at the produce market. Write an equation for the cost c of p pounds of potatoes. Equation: ___________________ c represents _______________ p represents _______________ 6. A cellular family phone plan cost $49 per month plus $0.05 per minute of long-distance service. Write an equation for the monthly bill b when m minutes of long-distance are used. Equation: ___________________ b represents _______________ m represents _______________ At the end of class today, I will be able to solve equations based on real world situations. Wait a minute . . . what the heck ? What if there’s a variable on both sides. What do I do ? When solving an equation, you will often be given an equation with variable on both sides and you will be asked to solve for one of them. FIRST Decide which variable you are solving for. How do I do this? Read the problem. FIRST Decide which variable you are solving for. SECOND Substitute the value for the variable you know into the equation. THIRD Get the variable you are solving for by itself. The Mudville Manatees won the league baseball championship. The manager of the souvenir shop wants to order special shirts and caps to sell to fans. She does market research and predicts the relationship between price in dollars p and number sold n. Shirts: n = 5,000 – 150p Caps: n = 3,000 – 100p What are the projected shirt sales if the price is $20 per shirt ? Shirts: n = 5,000 – 150p 1. What variable are you solving for? 2. What value does the equation give you ? 3. Substitute the value you know into the equation. 4. Get the variable you know by itself. What are the projected shirt sales if the price is $20 per shirt ? Shirts n = 5,000 – 150p Substitute If p=$20 n = 5,000 – 150 x 20 Solve n = 5,000 – 3,000 n = 2,000 shirts Suppose the manager wants to sell 3,500 shirts (n). How much should she charge for each shirt? Shirts: n = 5,000 – 150p 1. What variable are you solving for? 2. What value does the equation give you ? 3. Substitute the value you know into the equation. 4. Get the variable you know by itself. Suppose the manager wants to sell 3,500 shirts (n). How much should she charge for each shirt? Shirts: n = 5,000 – 150p Substitute If n = 3,500, then 3,500 = 5,000 – 150p Get the variable you are solving for by itself! 3,500 = 5,000 – 150p 3,500 – 5,000 = 5,000 – 5,000 – 150p -1,500 = -150p NOW WHAT ? Suppose the manager wants to sell 3,500 shirts (n). How much should she charge for each shirt? Get the variable you are solving for by itself! 3,500 = 5,000 – 150p 3,500 – 5,000 = 5,000 – 5,000 – 150p -1,500 = -150p -1,500 / -150 = -150p / -150 10 = p WHEN YOU ARE ISOLATING THE VARIABLE YOU ARE SOLVING FOR, REMEMBER YOU HAVE TO KEEP BALANCE You must remember to always do the same thing to both sides of the equation. THIS IS CALLED BALANCE. If you add to one side, you have to add the same amount to the other side. If you subtract from one side, you have to subtract the same amount to the other side. If you multiply or divide one side by a number, you have to divide or subtract the other side by the SAME number. A number divided by itself is equal to one. For example: 2 / 2 = 1 3/3=1 2.5 / 2.5 = 1 3.75 / 3.75 = 1 If a variable is multiplied by a number and you need to isolate it, you can divide both sides by the number. For example: = -150p -150 =p CROSS OUT THE LIKE NUMBERS What are the projected cap sales if the price is $17 per cap? Caps: n = 3,000 – 100p 1. What variable are you solving for? 2. What value does the equation give you ? 3. Substitute the value you know into the equation. 4. Get the variable you know by itself. What are the projected cap sales if the price is $17 per cap? Caps: n = 3,000 – 100p Substitute if p = $17 then, n = 3,000 – 100 x 17 Solve n = 3,000 – 100 x 17 n = 3,000 – 1,700 n = 1,300 Suppose the manager wants to sell 1,800 caps (n) How much should she charge for each cap ? Caps: n = 3,000 – 100p 1. What variable are you solving for? 2. What value does the equation give you ? 3. Substitute the value you know into the equation. 4. Get the variable you know by itself. Suppose the manager wants to sell 1,800 caps (n) How much should she charge for each cap ? Caps: n = 3,000 – 100p Substitute if n = 1,800 then, 1,800 = 3,000 – 100p Solve 1,800 = 3,000 – 100p 1,800 – 3,000 = 3,000 – 3,000 – 100p - 1,200 = - 100p -1,200 / -100 = -100p /-100 12 = p Break into pairs of two and work on the worksheet, Page 1. You have 12-1/2 minutes to work these problems. NOW, let’s work on page 2. You have 12-1/2 minutes to work these problems.