How can I show 1/3x+10=3/5x as or in a real world problem??
1/3 of a handyman’s fee plus an extra fee of 10 dollars for showing up, which is equal to 3/5 o his fee altogether. What is his fee in all with the extra fee
One-third of Leah's weekly pay check plus $10 = three-fifths of her check.
What is her weekly pay?
To show the equation 1/3x + 10 = 3/5x as a real-world problem, we need to come up with a scenario that can be represented by this equation. Let's consider the following situation:
Suppose you are planning a road trip. You estimate that you will be driving at a constant speed on a highway. Your speedometer shows your speed in miles per hour (mph). You want to determine the point where the distance you have covered becomes equal to the distance remaining to your destination.
Let's say x represents the time in hours that you have been driving. At any given time, the distance you have traveled can be represented by (1/3)x, as 1/3 represents the speed in miles covered per hour.
Initially, you start at mile marker 10, which we will use as a reference point. The equation includes the constant 10 to represent the initial distance you have already traveled.
Now, let's say the total distance to your destination is represented by 3/5x, as 3/5 represents the remaining distance to your destination per hour.
Therefore, the equation 1/3x + 10 = 3/5x can be interpreted as the point where the distance you have traveled (1/3x) plus the initial distance of 10 miles is equal to the remaining distance to your destination (3/5x).
By solving this equation, you can determine the time x when you will have covered exactly half of the total distance to your destination.
To show the equation 1/3x + 10 = 3/5x in a real-world problem, one way is to think about a scenario involving quantities that can be represented by the variables x and the given equation.
Let's say you are planning a road trip with your friends. You estimate that the trip will take x hours. However, you also know that for every hour you drive, you will need to stop and rest for 10 minutes.
In this scenario, we can represent the time you spend driving (x) in terms of hours, and the time you spend resting (10 minutes) in terms of hours as well. Remember that 1 hour is equal to 60 minutes.
To convert 10 minutes to hours, divide it by 60: 10 minutes ÷ 60 minutes/hour = 1/6 hour. Now we can rewrite the equation using this information:
1/3x + 1/6 = 3/5x
Now the equation represents the time you spend driving (1/3x) plus the time you spend resting (1/6) equalling the total estimated trip time (3/5x).