Question

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. discuss with a partner: 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 is $x - 0.1x+2.70 = 56.70$. Here, $x$ represents the original price of the jeans. First - simplify the left - hand side of the equation. $x-0.1x=(1 - 0.1)x = 0.9x$. So the equation becomes $0.9x+2.70 = 56.70$.

Step2: Solve for $x$

Subtract 2.70 from both sides of the equation:
$0.9x+2.70 - 2.70=56.70 - 2.70$.
$0.9x = 54$.
Then divide both sides by 0.9: $x=\frac{54}{0.9}=60$.

Step3: Verify solutions

For $x = 70$

Substitute $x = 70$ into the left - hand side of the original equation:
$70-0.1\times70 + 2.70=70 - 7+2.70=65.70
eq56.70$. So 70 is not a solution.

For $x = 60$

Substitute $x = 60$ into the left - hand side of the original equation:
$60-0.1\times60 + 2.70=60 - 6+2.70=56.70$. So 60 is the solution.

Step4: Interpret the solution

The original price of the jeans ($x$) is 60. The term $x-0.1x$ represents the price of the jeans after a 10% discount, and adding 2.70 (sales tax) gives the total price of 56.70.

Answer:

a. The solution $x = 60$ means the original price of the jeans before the 10% discount is 60. After applying a 10% discount ($0.1\times60 = 6$), the discounted price is $60 - 6=54$, and then adding the sales tax of 2.70 gives the total price of $54 + 2.70=56.70$.
b. To verify that 70 is not a solution and 60 is the solution:

• Substitute $x = 70$ into the equation $x-0.1x + 2.70$. We get $70-0.1\times70+2.70=70 - 7+2.70=65.70

eq56.70$, so 70 is not a solution.

• Substitute $x = 60$ into the equation $x-0.1x + 2.70$. We get $60-0.1\times60+2.70=60 - 6+2.70=56.70$, so 60 is the solution.