One real-world problem that can be modeled with the equation 4x + 5 = 17 is finding the cost of a certain item after applying a discount and sales tax.
Imagine you are shopping for a new pair of shoes. The regular price of the shoes is $17. The store is offering a 10% discount on all items. Additionally, there is a 6% sales tax applied to the discounted price.
To find out how much you will actually pay for the shoes, you can use the two-step equation 4x + 5 = 17. Let's break it down:
- In the equation, x represents the discounted price of the shoes.
- The first step is subtracting 5 from both sides of the equation: 4x + 5 - 5 = 17 - 5, which simplifies to 4x = 12.
- The second step is dividing both sides of the equation by 4 to isolate x: 4x/4 = 12/4, which simplifies to x = 3.
The solution x = 3 represents the discounted price of the shoes before adding sales tax. So, the discounted price of the shoes is $3.
To find out how much you will actually pay, you need to add the sales tax. The sales tax is 6% of the discounted price (or x). Therefore, you can multiply x by 0.06 and add this amount to x.
The final equation to find the actual cost of the shoes is: actual cost = x + 0.06x.
Plugging in x = 3 into the equation, we get: actual cost = 3 + 0.06(3) = 3 + 0.18 = $3.18.
Therefore, after applying the discount and sales tax, the actual cost of the shoes is $3.18.
write a real-world problem that you can model with the two-step equation 4x+5=17
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