### ACE Homework Answers

```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.
```