Question

Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run?

Select the two statements that are true.

(2 points)
Responses

Sam ran further than Dean.
Sam ran further than Dean.

The correct equation is s+2.3=6.8
The correct equation is s plus 2 point 3 is equal to 6 point 8

Dean ran further than Sam.
Dean ran further than Sam.

The correct equation is 2.3s=6.8
The correct equation is 2 point 3 s is equal to 6 point 8

The correct equation is s−2.3=6.8
The correct equation is s minus 2 point 3 is equal to 6 point 8

The boys ran the same distance.

Answer 1

To solve the problem, we need to find the distance Sam ran, given that Dean ran 2.3 kilometers fewer than Sam and that Dean ran 6.8 kilometers.

Let's denote the distance Sam ran as \( s \). According to the problem, we have:

\[ s - 2.3 = 6.8 \]

Now, to find the distance Sam ran, we can reorganize the equation:

\[ s = 6.8 + 2.3 \]
\[ s = 9.1 \text{ km} \]

Now, we can evaluate the statements:

1. **Sam ran further than Dean.** - True, since Sam ran 9.1 km while Dean ran 6.8 km.
2. **The correct equation is \( s + 2.3 = 6.8 \)** - False, because the correct equation is \( s - 2.3 = 6.8 \).
3. **Dean ran further than Sam.** - False, since Sam ran 9.1 km and Dean ran 6.8 km.
4. **The correct equation is \( 2.3s = 6.8 \)** - False, as this does not represent the relationship given in the problem.
5. **The correct equation is \( s - 2.3 = 6.8 \)** - True, this correctly represents the problem.
6. **The boys ran the same distance.** - False, as Dean ran 6.8 km and Sam ran 9.1 km.

Therefore, the two true statements are:

1. Sam ran further than Dean.
2. The correct equation is \( s - 2.3 = 6.8 \).