Question

lesson 6 - aspire to do
inquiry activity worksheet algebra 1 unit 2
6.3 whats acceptable?
directions: find 1 classmate to work with, if possible. collect a calculator. in problems 2 and 3, you will
see a series of equations that are related to the original equation from the launch and that can be
interpreted in terms of the situation. for each question, your job is to determine either what move was
made to the original equation, or what the equation means in context. then, you should check if the
equation has the same solution as the original.
launch: noah is buying a pair of jeans and using a coupon for 10% off. the total price is $56.70, which
includes $2.70 in sales tax. noahs purchase can be modeled by the equation:
$x - 0.1x + 2.70 = 56.70$
how does the equation represent noahs purchase?

1. discuss with a partner and record your answers:

a. what does the solution to the equation mean in this situation?
b. how can you verify that 70 is not a solution but 60 is the solution?

Explanation:

Step1: Analyze the equation

The equation \(x - 0.1x+2.70 = 56.70\) represents Noah's purchase. Here, \(x\) is the original price of the jeans. \(0.1x\) is the discount (10% of the original price). \(x - 0.1x\) is the price after discount. Then adding the sales - tax (\(2.70\)) gives the total price (\(56.70\)).

Step2: Solve the equation

First, simplify the left - hand side of the equation:

$$
LATEXBLOCK0
$$

Subtract \(2.70\) from both sides:

$$
LATEXBLOCK1
$$

Divide both sides by \(0.9\):

$$x=\frac{54}{0.9}=60$$

Step3: Verify the solutions

For \(x = 70\)

Substitute \(x = 70\) into the left - hand side of the equation \(x-0.1x + 2.70\):

$$
LATEXBLOCK2
$$

For \(x = 60\)

Substitute \(x = 60\) into the left - hand side of the equation \(x-0.1x + 2.70\):

$$
LATEXBLOCK3
$$

Answer:

a. The solution \(x = 60\) means that the original price of the pair of jeans Noah bought is \(\$60\).
b. When \(x = 70\), \(x-0.1x + 2.70=70-7 + 2.70 = 65.70
eq56.70\). When \(x = 60\), \(x-0.1x + 2.70=60 - 6+2.70=56.70\). So \(70\) is not a solution and \(60\) is the solution.