...................................................................................Triana is on a 120-mile four-day bike ride. On the first day she travels 24 miles. She would like to travel equal amounts over the remaining three days. How far will she travel on each of those three days? Write and solve an equation of the form px+q=r . Then write a sentence to explain your answer.
Let's assume Triana travels the same distance each day after the first day, and let's call that distance x. Therefore, on the second day, she will travel x miles, on the third day, she will travel x miles again, and on the fourth day, she will travel x miles once more.
The total distance she will travel in the four days is the sum of the distance she traveled on the first day (24 miles) and the distance she will travel on the remaining three days (3x miles). We can express this using the equation:
24 + 3x = 120
To solve for x, we need to isolate it on one side of the equation. Subtracting 24 from both sides gives:
3x = 120 - 24
3x = 96
Now, we can solve for x by dividing both sides by 3:
3x/3 = 96/3
x = 32
Therefore, Triana will travel 32 miles each day on the second, third, and fourth days of her bike ride.
To find out how far Triana will travel on each of the remaining three days, we can let the distance traveled on each of those three days be represented by the variable x.
On the first day, Triana travels 24 miles. Over the next three days, she wants to travel equal amounts. Therefore, the total distance she will travel on the remaining three days will be 3x.
Adding the distance traveled on the first day (24 miles) to the total distance traveled on the remaining three days (3x) should give us the total distance of 120 miles.
Therefore, we can set up the equation: 24 + 3x = 120
To solve for x, we need to isolate x. First, subtract 24 from both sides of the equation:
3x = 120 - 24
Simplifying further:
3x = 96
Finally, divide both sides of the equation by 3 to solve for x:
x = 96 / 3
x = 32
Hence, Triana will travel 32 miles on each of the remaining three days.
To find out how far Triana will travel on each of the remaining three days, we can start by calculating the total distance she needs to cover on those days by subtracting the distance covered on the first day from the total distance of the bike ride.
Total distance to cover on the remaining three days = Total distance of bike ride - Distance covered on the first day
= 120 miles - 24 miles
= 96 miles
Since Triana wants to travel equal amounts over the remaining three days, we can represent the distance she will travel on each of those days as "x" miles. Therefore, the equation to represent this situation is:
3x = 96
Now we can solve the equation to find the value of x:
Divide both sides of the equation by 3:
3x / 3 = 96 / 3
x = 32
The solution to the equation is x = 32. It means that Triana will travel 32 miles on each of the remaining three days.
Therefore, Triana will travel 32 miles on each of the three remaining days of her bike ride.