On a recent road trip, Orlando drove an unknown number of miles during his first week. He then drove fifteen more miles in his second week and twenty-five fewer miles in his third week when compared to the first week. Write an expression that represents the total number of miles that Orlando drove in the 3-week road trip.
Step 1: Translate Given Information into Algebra Expression
For this question, we are looking to write an expression to represent a certain total. The starting amount will be an unknown amount and every other amount will be written in terms of the initial amount.
In the given prompt, we know that Orlando drove an unknown number of miles during his first week, so the number of miles he drove that week will be assigned a variable (x).
Number of miles driven first week → x
We are also given that Orlando drove fifteen more miles in his second week in comparison to the number he drove the first week. This means,
Number of miles driven second week → x + 15
Finally, we are told that he drove twenty-five fewer miles in his third week when compared to the first week. Since he drove fewer miles, this means we will be subtracting 25 miles from the amount he drove the first week which is represented by x.
Number of miles driven third week → x – 25
Step 2: Determine Total
Now that we have all individual expressions, we can find the final sum.
We are asked to write an expression that represents the total number of miles that Orlando drove in the 3-week road trip. To find the total, we need to find the expression that adds all expressions and simplify.
x+ x + 15 + x – 25
We can now rearrange the expression to group like terms together. Remember to include the sign IN FRONT of a term.
x + x + 15 + x – 25
x + x + x + 15 – 25
The expression becomes::
3x – 10