# A.2.6.3 What's Acceptable?

- Author:
- Katie Akesson

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. Noah's purchase can be modeled by the equation:
* x* - 0.1*x*+ 2.70 = 56.70
Explain how the equation represents Noah's purchase

What does the solution to the equation mean in this situation?

How can you verify that 70 is not a solution but 60 is the solution?

*x*- 0.1

*x*+ 2.70 = 56.70. Each equation is a result of performing one or more algebraic moves on that original equation. Each can also be interpreted in terms of Noah’s purchase. For each equation do the following: a. determine either what move was made b. how the equation could be interpreted. c. check if 60 is the solution of the equation. [either a. or b. is answered for you in square brackets, Equation A is done completely for you for as an example]

**100x - 10x +270 = 5,670 a. What was done? [Multiply each side by 100.] b. Interpretation? [The price is expressed in cents instead of dollars.] c. Is 60 the solution? [Yes]**

__Equation A____Equation B__*
x* - 0.1*x* = 54
a. What was done? [Subtract 2.70 from both sides of the equation.]
b. Interpretation?
c. Is 60 the solution?

** Equation C**
0.9x + 2.70 = 56.70
a. What was done?
b. Interpretation? [10% off means paying 90% of the original price. 90% of the original price plus sales tax is $56.70.]
c. Is 60 the solution?

Here are some other equations. For each equation, determine what move was made or how the equation could be interpreted. Then, check if 60 is the solution to the equation.
** Equation D**
x - 0.1x = 56.70
a. What was done?
b. Interpretation? [The price after using the coupon for 10% off and before sales tax is $56.70.]
c. Is 60 the solution?

** Equation E**
x - 0.1x = 59.40
a. What was done? [Subtract 2.70 from the left and add 2.70 to the right.]
b. Interpretation?
c. Is 60 the solution?

** Equation F**
2(x - 0.1x + 2.70) = 56.70
a. What was done?
b. Interpretation? [The price of 2 pairs of jeans, after using the coupon for 10% off and paying sales tax, is $56.70.]
c. Is 60 the solution?

Which of the six equations are equivalent to the original equation? Explain how you know.