Math  /  Algebra

QuestionProblem 3: Last season two running backs on the College football team rushed for a combined 1550 yards. One rushed 4 times as many yards as the other. How many yards did the player with the most yards rush? \begin{tabular}{|c|c|c|c|c|c|} \hline Answer & 310 & 640 & 930 & 1175 & 1240 \\ \hline Code & A & B & C & D & E \\ \hline \end{tabular} \square

Studdy Solution

STEP 1

What is this asking? Two players ran a total of 1550 yards, and one ran 4 times more than the other.
How many yards did the better player run? Watch out! Don't mix up the total yards and the yards of each player!

STEP 2

1. Set up variables
2. Create an equation
3. Solve for xx
4. Calculate the yards of the better player

STEP 3

Let's call the yards of the player who ran *less* xx.
Since the other player ran **4 times** more, their yards are 4x4 \cdot x or 4x4x.

STEP 4

We know that the **total yards** are 1550.
So, the yards of the first player (xx) *plus* the yards of the second player (4x4x) *equals* 1550.
We can write this as an equation: x+4x=1550x + 4x = 1550

STEP 5

**Combine** the xx terms on the left side: 5x=15505x = 1550

STEP 6

To **isolate** xx, we need to **divide both sides** of the equation by 5.
Remember, what we do to one side, we *must* do to the other! 5x5=15505 \frac{5x}{5} = \frac{1550}{5} x=310 x = 310 So, the player who ran *less* ran 310 yards.

STEP 7

We know the better player ran 4x4x yards.
Since we found x=310x = 310, we can **substitute** that value back in: 4x=4310=1240 4 \cdot x = 4 \cdot 310 = 1240

STEP 8

The player with the most yards rushed for **1240** yards.
That corresponds to answer choice **E**!

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