Alex, Blake and Charlie play a computer game. Alex goes first and scores n points. - Blake scores 8 points less than 3 times the number of points scored by Alex. - Charlie scores 25 more points than Blake. - The three people score a total of 618 points. Work out how many points they each score. You must show your working.

GCSE OCR Maths Solving equations: Alex, Blake and Charlie play a c

Alex, Blake and Charlie play a computer game - OCR - GCSE Maths - Question 10 - 2021 - Paper 1

Question 10

Alex, Blake and Charlie play a computer game. Alex goes first and scores n points. - Blake scores 8 points less than 3 times the number of points scored by Alex. -... show full transcript

Worked Solution & Example Answer:Alex, Blake and Charlie play a computer game - OCR - GCSE Maths - Question 10 - 2021 - Paper 1

Step 1

Define the Variables

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Answer

Let Alex's score be represented by $n$ .

Then, Blake's score can be expressed as:
$B = 3n - 8$
where $B$ is Blake's score.

Next, Charlie's score can be represented as:
$C = B + 25 = (3n - 8) + 25 = 3n + 17$
where $C$ is Charlie's score.

Step 2

Set Up the Equation for Total Points

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According to the information given, the total score of all three players is 618 points:

$n + B + C = 618$
Substituting the expressions for Blake's and Charlie's scores:

$n + (3n - 8) + (3n + 17) = 618$

Step 3

Simplify the Equation

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Answer

Combining like terms gives:

$n + 3n - 8 + 3n + 17 = 618$
$7n + 9 = 618$

Step 4

Solve for n

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Answer

Subtract 9 from both sides:

$7n = 609$
Now, divide by 7:

$n = rac{609}{7} = 87$ .

Thus, Alex scored 87 points.

Step 5

Calculate Blake's Score

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Answer

Substituting the value of $n$ into Blake's score formula:

$B = 3(87) - 8 = 261 - 8 = 253$ .

So, Blake scored 253 points.

Step 6

Calculate Charlie's Score

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Answer

Now substituting the value of Blake's score into Charlie's score formula:

$C = 253 + 25 = 278$ .

So, Charlie scored 278 points.

Step 7

Final Results

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Answer

To summarize their scores:

Alex: 87 points
Blake: 253 points
Charlie: 278 points.

Alex, Blake and Charlie play a computer game - OCR - GCSE Maths - Question 10 - 2021 - Paper 1

Worked Solution & Example Answer:Alex, Blake and Charlie play a computer game - OCR - GCSE Maths - Question 10 - 2021 - Paper 1

Define the Variables

Set Up the Equation for Total Points

Simplify the Equation

Solve for n

Calculate Blake's Score

Calculate Charlie's Score

Final Results

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