Answer:
See below.
Step-by-step explanation:
So, we know that Noah's purchase can be modeled by the equation:
[tex]x-0.1x+2.70=56.70[/tex]
Part 1)
The solution to the equation will be the value of x.
In this case, x will represent the original price of the jeans.
We know that Noah has a coupon for 10% off the original price of the jeans.
So, 0.1x will represent how much of the original price Noah gets a a discount on.
Therefore, (x - 0.1x) represents the total cost of the jeans after the coupon.
So, x is our original price of the jeans.
Part 2)
To verify that 70 is not a solution, we can simply substitute 70 for x and check whether or not the equation is true. So:
[tex](70)-0.1(70)+2.7\stackrel{?}{=}56.70[/tex]
Multiply:
[tex]70-7+2.7\stackrel{?}{=}56.7[/tex]
Subtract:
[tex]63+2.7\stackrel{?}{=}56.7[/tex]
Add:
[tex]65.7\neq56.7[/tex]
However, we can verify that 60 is the solution by substituting. So, substitute 60 for every x:
[tex](60)-0.1(60)+2.7\stackrel{?}{=}5.7[/tex]
Multiply:
[tex]60-6+2.7\stackrel{?}{=}56.7[/tex]
Subtract:
[tex]54+2.7\stackrel{?}{=}56.7[/tex]
Add:
[tex]56.7\stackrel{\checkmark}{=}56.7[/tex]
So, 60 is indeed the solution and is the value of x.
So, this means that $60 was the original price of the jeans.
