Question

The sum of two numbers is 100. The different between them is 56. What is the larger number?

Answer 1

Answer:-

$\pink{\bigstar}$ The larger number is $\large\leadsto\boxed{\tt\purple{78}}$

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• Given:-

• Sum of two numbers is 100.

• Difference between the numbers is 56.

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• To Find:-

• The larger number = ?

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• Solution:-

Let the two numbers be 'x' and 'y' respectively.

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According to the question:-

✯ Sum of two numbers is 100.

➪ $\sf x + y = 100 \dashrightarrow\bold\red{[equation \: 1]}$

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Also,

✯ Difference between the numbers is 56.

➪ $\sf x - y = 100 \dashrightarrow\bold\red{[equation \: 2]}$

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• Adding equation [1] and equation [2]:-

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➪ $\sf (x + y) + (x - y) = 100 + 56$

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➪ $\sf x + y + x - y = 156$

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➪ $\sf 2x = 156$

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➪ $\sf x = \dfrac{156}{2}$

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★ $\large{\bold\red{x = 78}}$

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• Substituting the value of x in equation [1]:-

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➪ $\sf x + y = 100$

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➪ $\sf 78 + y = 100$

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➪ $\sf y = 100 - 78$

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★ $\large{\bold\red{y = 22}}$

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Therefore, the numbers are 78 and 22.

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The larger number is 78.