Question

noah is buying a pair of jeans and using a coupon for 10% off. the total price is $56.70, which includes sales tax.
noahs purchase can be modeled by the equation:
x - 0.1x + 2.70 = 56.70

1. discuss with a partner:

a. what does the solution to the equation mean in this situation?

Explanation:

Step1: Simplify the left - hand side of the equation

Combine like terms in \(x - 0.1x+2.70\). Using the distributive property \(ax+bx=(a + b)x\), we have \((1 - 0.1)x+2.70=0.9x + 2.70\). So the equation becomes \(0.9x+2.70 = 56.70\).

Step2: Isolate the term with \(x\)

Subtract \(2.70\) from both sides of the equation. Using the subtraction property of equality \(0.9x+2.70-2.70=56.70 - 2.70\), which simplifies to \(0.9x=54\).

Step3: Solve for \(x\)

Divide both sides of the equation by \(0.9\). Using the division property of equality \(\frac{0.9x}{0.9}=\frac{54}{0.9}\), we get \(x = 60\).

In the context of the problem, \(x\) represents the original price of the pair of jeans before the \(10\%\) discount. The solution \(x = 60\) means that the original price of the jeans (before applying the \(10\%\) - off coupon) is \(\$60\).

Answer:

The solution \(x = 60\) means that the original price of the jeans (before the \(10\%\) discount) is \(\$60\).