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 modelled by the equation
x-0.1x+2.70=56.70
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?

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.

Answer:

$60

Step-by-step explanation:

i did it on paper

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