Page 628 - Basic College Mathematics with Early Integers

GROUP ACTIVITY 605

In real estate, a house’s selling price P is found by adding the real estate agent’s commission C to the amount A that the
seller of the house receives: P = A + C.

75. A house sold for $230,000.The owner’s real estate 76. A homeowner plans to use a real estate agent to sell
agent received a commission of $13,800. How much his house. He hopes to sell the house for $165,000
did the seller receive? (Hint: Substitute the known and keep $156,750 of that. If everything goes as he
values into the equation, then solve the equation for has planned, how much will his real estate agent
the remaining unknown.) receive as a commission?

In retailing, the retail price P of an item can be computed using the equation P = C + M , where C is the wholesale cost
of the item and M is the amount of markup.

77. The retail price of a computer system is $999 after a 78. Slidell Feed and Seed sells a bag of cat food for $12.
markup of $450.What is the wholesale cost of the If the store paid $7 for the cat food, what is the
computer system? (Hint: Substitute the known markup on the cat food?
values into the equation, then solve the equation for
the remaining unknown.)

Chapter 8 Group Activity

Modeling Equation Solving with Addition We are left with the following model, which represents
and Subtraction the solution, x =-3.
Sections 8.1–8.4 x
We can use positive counters and negative counters
to help us model the equation-solving process. We also Similarly, we can represent the equation x - 4 =-6
need to use an object that represents a variable. We use as follows:
small slips of paper with the variable name written on
them. x
Recall that taking a and together creates a neu-
tral or zero pair. After a neutral pair has been formed, it To get the variable by itself, we must remove 4 red coun-
can be removed from or added to an equation model ters from both sides of the model
without changing the overall value. We also need to
remember that we can add or remove the same number x
of positive or negative counters from both sides of an
equation without changing the overall value. We are left with the following model, which represents
We can represent the equation x + 5 = 2 as follows: the solution, x =-2.

x x

To get the variable by itself, we must remove 5 black
Use the counter model to solve each equation.
counters from both sides of the model. Because there
are only 2 counters on the right side, we must add 5 neg- 1. x - 3 =-7 2. x - 1 =-9
ative counters to both sides of the model. Then we can 3. x + 2 = 8 4. x + 4 = 5
remove neutral pairs: 5 from the left side and 2 from the
5. x + 8 = 3 6. x - 5 =-1
right side.
7. x - 2 = 1 8. x - 5 = 10
9. x + 3 =-7 10. x + 8 =-2
x