Math / Algebra

Question7. A baseball player has (13) base hits out of 57 ) at bats for a current batting average of 2.228) How many consecutive base hits does he need if he wants to raise his batting average to 0.475 ? $\begin{array}{l} 13+x=0.228(57+x) \\ 13+x=12.996+0.228 x \\ -12.996=12.926 \\ \begin{aligned} 0.004+x & =0.228 x \\ -x & -1 x \end{aligned} \\ \frac{0.004}{-0.772}=-\frac{.772 / 4}{-8.7} \\ -0.772 \quad-\not .772 \end{array}$

Studdy Solution

STEP 1

1. The baseball player currently has 13 base hits out of 57 at bats.
2. The current batting average is 0.228.
3. The player wants to raise the batting average to 0.475.
4. We need to find how many consecutive base hits are required to achieve this new average.

STEP 2

1. Define variables for the problem.
2. Set up an equation for the current batting average.
3. Set up an equation for the desired batting average.
4. Solve the equation to find the number of consecutive base hits needed.

STEP 3

Define variables for the problem.
Let $x$ be the number of consecutive base hits needed.

STEP 4

Set up an equation for the current batting average.
The current batting average is calculated by dividing the number of base hits by the number of at bats:
$\frac{13}{57} = 0.228$

STEP 5

Set up an equation for the desired batting average.
The desired batting average is 0.475, so we need to find $x$ such that:
$\frac{13 + x}{57 + x} = 0.475$

STEP 6

Solve the equation to find the number of consecutive base hits needed.
Multiply both sides by $57 + x$ to eliminate the fraction:
$13 + x = 0.475(57 + x)$
Distribute the 0.475:
$13 + x = 27.075 + 0.475x$
Rearrange the equation to isolate $x$ :
$x - 0.475x = 27.075 - 13$
Combine like terms:
$0.525x = 14.075$
Divide both sides by 0.525 to solve for $x$ :
$x = \frac{14.075}{0.525}$
Calculate the value:
$x \approx 26.81$
Since $x$ must be a whole number, round up to the nearest whole number:
The player needs $\boxed{27}$ consecutive base hits to achieve the desired batting average.

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Studdy Solution

STEP 1

1. The baseball player currently has 13 base hits out of 57 at bats.
2. The current batting average is 0.228.
3. The player wants to raise the batting average to 0.475.
4. We need to find how many consecutive base hits are required to achieve this new average.

STEP 2

1. Define variables for the problem.
2. Set up an equation for the current batting average.
3. Set up an equation for the desired batting average.
4. Solve the equation to find the number of consecutive base hits needed.

STEP 3

Define variables for the problem.
Let $x$ be the number of consecutive base hits needed.

STEP 4

Set up an equation for the current batting average.
The current batting average is calculated by dividing the number of base hits by the number of at bats:
$\frac{13}{57} = 0.228$

STEP 5

Set up an equation for the desired batting average.
The desired batting average is 0.475, so we need to find $x$ such that:
$\frac{13 + x}{57 + x} = 0.475$

STEP 6

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Studdy Solution

STEP 1

1. The baseball player currently has 13 base hits out of 57 at bats.2. The current batting average is 0.228.3. The player wants to raise the batting average to 0.475.4. We need to find how many consecutive base hits are required to achieve this new average.

STEP 2

1. Define variables for the problem.2. Set up an equation for the current batting average.3. Set up an equation for the desired batting average.4. Solve the equation to find the number of consecutive base hits needed.

STEP 3

Define variables for the problem.Let x x x be the number of consecutive base hits needed.

STEP 4

Set up an equation for the current batting average.The current batting average is calculated by dividing the number of base hits by the number of at bats:1357=0.228 \frac{13}{57} = 0.228 5713​=0.228

STEP 5

Set up an equation for the desired batting average.The desired batting average is 0.475, so we need to find x x x such that:13+x57+x=0.475 \frac{13 + x}{57 + x} = 0.475 57+x13+x​=0.475

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The baseball player currently has 13 base hits out of 57 at bats.
2. The current batting average is 0.228.
3. The player wants to raise the batting average to 0.475.
4. We need to find how many consecutive base hits are required to achieve this new average.

1. Define variables for the problem.
2. Set up an equation for the current batting average.
3. Set up an equation for the desired batting average.
4. Solve the equation to find the number of consecutive base hits needed.

Define variables for the problem.
Let $x$ be the number of consecutive base hits needed.

Set up an equation for the current batting average.
The current batting average is calculated by dividing the number of base hits by the number of at bats:
$\frac{13}{57} = 0.228$

Set up an equation for the desired batting average.
The desired batting average is 0.475, so we need to find $x$ such that:
$\frac{13 + x}{57 + x} = 0.475$