On Monday, Maggie ran n miles. On Tuesday, she ran 90% of the number of miles that she ran on Monday. On Wednesday, she ran 50% of the number of miles that she ran on Tuesday.

Question

Question
Move a symbol to the box and expressions to the blanks to create two equivalent expressions that represent the total number of miles Maggie ran on Monday, Tuesday, and Wednesday.

Response area with 3 blank spaces
First expression: n plus 0.9 n
Blank space 1 empty

Blank space 2 empty


Second expression:
Blank space 4 empty
n

Answer 1

To create two equivalent expressions representing the total number of miles Maggie ran over the three days, we first need to calculate the total miles she ran on each day:

1. On Monday: she ran \( n \) miles.
2. On Tuesday: she ran \( 90% \) of Monday's miles, which is \( 0.9n \).
3. On Wednesday: she ran \( 50% \) of Tuesday's miles, which is \( 0.5 \times 0.9n = 0.45n \).

Now we can sum these up to find the total miles Maggie ran:

Total miles = Miles on Monday + Miles on Tuesday + Miles on Wednesday
Total miles = \( n + 0.9n + 0.45n \).

Now we can combine these terms:

Total miles = \( n + 0.9n + 0.45n = (1 + 0.9 + 0.45)n = 2.35n \).

Now, we can fill in the response area with the equivalent expressions:

Response area

First expression:
\( n + 0.9n \)
Blank space 1: \( + 0.45n \)
Blank space 2: \( = 2.35n \)

Second expression:
Blank space 4: \( 2.35 \)
\( n \)

So the completed area looks like this:

First expression: \( n + 0.9n \)
Blank space 1: \( + 0.45n \)
Blank space 2: \( = 2.35n \)

Second expression:
Blank space 4: \( 2.35 \)
\( n \)