The sum of two numbers is $550$ . If $3.5$ of the number is equal to $7.5$ of the other, find the numbers.

325

and

225

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375

and

175

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200

and

350

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None of the above.

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Solution

The correct option is A $375$ and $175$
Let the first number be $x$ .
Then, the other number will be $550 - x$ .
By the given condition, we have
$3.5 \times x = 7.5 \times (550 - x)$

$⟹ \frac{35}{10} \times x = \frac{75}{10} (550 - x)$

$⟹ 35 x = (75 \times 550) - 75 x$

$⟶ 35 x + 75 x = 41250$

$⟹ 110 x = 41250$

$⟹ x = \frac{41250}{110}$

$⟹ x = 375$

The first number $= 550 - 375$ = $175$
So, option B is correct.

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If the sum of two consecutive numbers is 71 and the smaller number is x, find the other number.

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