write a real-world problem that you can model with the two-step equation 4x+5=17
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.
A real-world problem that can be modeled with the two-step equation 4x + 5 = 17 is a situation where a person wants to determine how many hours they need to work to reach a certain amount of money.
Let's say the person wants to earn $17 and their hourly wage is $4. By using the equation 4x + 5 = 17, we can represent this situation.
Solution:
Step 1: Subtract 5 from both sides of the equation.
4x + 5 - 5 = 17 - 5
4x = 12
Step 2: Divide both sides of the equation by 4.
4x/4 = 12/4
x = 3
Therefore, the solution shows that the person needs to work 3 hours to earn $17 in this scenario.
Sure, here's a real-world problem that can be modeled using the two-step equation 4x + 5 = 17:
The problem: Anna has been saving money to buy a new video game that costs $17. She has already saved some money but wants to know how much more she needs to save in order to reach her goal.
Explanation:
Step 1: Define the variable
To model the problem with the equation, we will let 'x' represent the amount of money Anna still needs to save.
Step 2: Translate the problem into an equation
According to the problem, the price of the video game ($17) is equal to the amount that Anna has already saved (4x) plus an additional $5.
So, the equation becomes: 4x + 5 = 17.
Step 3: Solve the equation
To solve the equation, we want to isolate 'x' on one side.
Start by subtracting 5 from both sides of the equation:
4x + 5 - 5 = 17 - 5.
This simplifies to: 4x = 12.
Next, we divide both sides of the equation by 4 to solve for 'x':
4x/4 = 12/4.
This gives us: x = 3.
Step 4: Interpret the solution
The solution, x = 3, tells us that Anna still needs to save $3 in order to reach her goal of $17.
So, the real-world problem modeled by the equation 4x + 5 = 17 is that Anna needs to determine how much more money she needs to save to buy a $17 video game, given that she has already saved some money.