Can you please show me how choose the right answer and how to get the right answer.
Which problem situation matches the equation below?
5x+5(x+20)=500
F. five people contributed to a fundraiser each give $20 more than the basic amount requested. In all, the amount contributed by these people totaled $500. What was the basic amount requested?
G. Jamal opened two investment amounts, each with 5% simple interest per year. In one, he deposited $20 more than in the other. Together, at the end of one year, the two accounts earned $500. How much had he deposited in each account?
H. A passenger train and a freight train leave the same station at the same time and go in opposite directions, the passenger train going 20 per hour faster than the freight train. At the end of 5 hours, the trains are 500 miles apart. Find the speed of the freight train.
J. A passenger train and a freight train are 500 miles apart and travel toward each other on parallel tracks. The speed of the passenger train is 20 miles per hour faster than that of the freight train. The freight train is moving at a rate of 40 miles per hour. How long will it take the two trains to pass each other?
Try writing an equation for each problem. It's easy to make a mistake while glancing over the answer choices.
Derive an Eq for the 1st prob. If it
does not match, set-up the next problem. Continue until you find the Eq
that matches.
F. Amt requested = X dollars,
Amt ea gave = (X + 20) dollars,
Eq: 5(X + 20) = 500. Not a match.
G. 1st acc. inv. X dollers.
2nd acc. inv. (X + 20) dollars.
0.05X + 0.05(X + 20) = 500.
Multiply both sides by 100 to eliminate decimals.
Eq:5X + 5(X + 20) = 50000. Not a match.
H. Freight Train speed = X mi/h.
Pass. Train speed = (X + 20)mi/h.
d1 + d2 = 500.
Eq: SX + 5(X + 20) = 500. This is it!
To choose the right answer and get the right answer, you need to solve the equation and see which problem situation matches the equation.
First, let's simplify the equation:
5x + 5(x + 20) = 500
Distribute the 5 to the terms inside the parentheses:
5x + 5x + 100 = 500
Combine like terms:
10x + 100 = 500
Next, isolate the variable by subtracting 100 from both sides:
10x = 400
Finally, divide both sides by 10 to solve for x:
x = 40
Now that we have the value of x, which is 40, we can analyze the problem situations to see which one matches the equation.
F. The equation does not involve any basic amount requested, so it does not match.
G. The equation does involve two investment amounts, but it does not match the equation as there is no mention of 5x or x + 20.
H. The equation does involve the speed of the freight train (x) and the speed of the passenger train being 20 per hour faster (x + 20), but it does not match the equation as there is no mention of trains being 500 miles apart after 5 hours.
J. The equation does involve the speed of the freight train (x) and the speed of the passenger train being 20 per hour faster (x + 20), and it also mentions that the trains are 500 miles apart. However, it does not match the equation as there is no mention of how long it will take the two trains to pass each other.
Therefore, the problem situation that matches the equation is option G. Jamal opened two investment amounts, each with 5% simple interest per year. In one, he deposited $20 more than in the other. Together, at the end of one year, the two accounts earned $500. How much had he deposited in each account?