Warm Up 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 _______________
Transcript
Warm UpExpress 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.
Warm UpExpress 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 _______________
Warm UpExpress 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 _______________
Objective
At the end of class today, I will be able to solve equations based on real world situations.
Solving EquationsWait 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.
Solving EquationsFIRST 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.
Let’s Look at the HomeworkThe 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
Let’s Look at the HomeworkWhat 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.
Let’s Look at the HomeworkWhat 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
Let’s Look at the HomeworkSuppose 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.
Let’s Look at the HomeworkSuppose 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 ?
Let’s Look at the HomeworkSuppose 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
BALANCEWHEN 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.
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.
ONE MORE THING A number divided by itself is equal to one.
For example: 2 / 2 = 1 2.5 / 2.5 = 1
3 / 3 = 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
= pCROSS OUT
THE LIKE NUMBERS
Let’s Look at the HomeworkWhat 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.
Let’s Look at the HomeworkWhat 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
Let’s Look at the HomeworkSuppose 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.
Let’s Look at the HomeworkSuppose 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
GROUP WORKBreak into pairs of two and work on the worksheet, Page 1.
