Question

a cricket player scored 180 runs in the first match and257 runs in the second match .find the number of runs he should score in the third match, so that the average of runs in three matches be 230

Answer 1

Answer :-

• The cricket player should score 253 runs in the third match, so that the average of the three matches becomes 230.

Given :-

• A cricket player scored 180 runs in the first match.
• He scored 257 runs in the second match.

To find :-

• The number of runs he should score in the third match, so that the average of runs in three matches becomes 230.

Step-by-step explanation :-

• Let's find the number of runs the cricket player should score in the third match!

We know that :-

$\underline{\boxed{\sf Average = \dfrac{Sum \: of \: all \: values}{Number \: of \: values}}}$

Here,

• Runs scored in the first match = 180.
• Runs scored in the second match = 257.

Now,

• Let the number of runs scored in the third match be x.

• Then the sum of all values = 180 + 257 + x.

• And the number of values is 3.
• The average is 230.

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Substituting the given values in this formula,

$\bf 230 = \dfrac{180 + 257 + x}{3}$

Transposing 3 from RHS to LHS, changing it's sign,

$\bf 230 \times 3 = 180 + 257 + x$

Multiplying 230 with 3,

$\bf 690 = 180 + 257 + x$

Adding 257 to 180,

$\bf 690 = 437 + x$

Transposing 437 from RHS to LHS, changing it's sign,

$\bf 690 - 437 = x$

Subtracting 437 from 690,

$\overline{\boxed{\bf 253 = x}}$

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• Hence, the cricket player should score 253 runs in the third match.