<h2><u>An</u><u>swer</u><u>:</u><u>-</u></h2>
The larger number is ![\large\leadsto\boxed{\tt\purple{78}}](https://tex.z-dn.net/?f=%5Clarge%5Cleadsto%5Cboxed%7B%5Ctt%5Cpurple%7B78%7D%7D)
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<h3>• <u>Given</u><u>:</u><u>-</u></h3>
- Sum of two numbers is 100.
- Difference between the numbers is 56.
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<h3>
• <u>To</u><u> </u><u>Find</u><u>:</u><u>-</u></h3>
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<h3>
• <u>Solut</u><u>ion</u><u>:</u><u>-</u></h3>
Let the two numbers be 'x' and 'y' respectively.
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<u>According to the question:-</u>
✯ Sum of two numbers is 100.
➪ ![\sf x + y = 100 \dashrightarrow\bold\red{[equation \: 1]}](https://tex.z-dn.net/?f=%5Csf%20x%20%2B%20y%20%3D%20100%20%5Cdashrightarrow%5Cbold%5Cred%7B%5Bequation%20%5C%3A%201%5D%7D)
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Also,
✯ Difference between the numbers is 56.
➪ ![\sf x - y = 100 \dashrightarrow\bold\red{[equation \: 2]}](https://tex.z-dn.net/?f=%5Csf%20x%20-%20y%20%3D%20100%20%5Cdashrightarrow%5Cbold%5Cred%7B%5Bequation%20%5C%3A%202%5D%7D)
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• <u>Adding</u><u> </u><u>eq</u><u>uation</u><u> </u><u>[</u><u>1</u><u>]</u><u> </u><u>a</u><u>nd</u><u> </u><u>equat</u><u>ion</u><u> [</u><u>2</u><u>]</u><u>:</u><u>-</u>
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➪ ![\sf (x + y) + (x - y) = 100 + 56](https://tex.z-dn.net/?f=%5Csf%20%28x%20%2B%20y%29%20%2B%20%28x%20-%20y%29%20%3D%20100%20%2B%2056)
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➪ ![\sf x + y + x - y = 156](https://tex.z-dn.net/?f=%5Csf%20x%20%2B%20y%20%2B%20x%20-%20y%20%3D%20156)
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➪ ![\sf 2x = 156](https://tex.z-dn.net/?f=%5Csf%202x%20%3D%20156)
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➪ ![\sf x = \dfrac{156}{2}](https://tex.z-dn.net/?f=%5Csf%20x%20%3D%20%5Cdfrac%7B156%7D%7B2%7D)
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★ ![\large{\bold\red{x = 78}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cbold%5Cred%7Bx%20%3D%2078%7D%7D)
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• <u>Subst</u><u>ituting</u><u> </u><u>the</u><u> </u><u>va</u><u>lue</u><u> </u><u>of</u><u> </u><u>x</u><u> </u><u>in</u><u> </u><u>equa</u><u>tion</u><u> </u><u>[</u><u>1</u><u>]</u><u>:</u><u>-</u>
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➪ ![\sf x + y = 100](https://tex.z-dn.net/?f=%5Csf%20x%20%2B%20y%20%3D%20100)
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➪ ![\sf 78 + y = 100](https://tex.z-dn.net/?f=%5Csf%2078%20%2B%20y%20%3D%20100)
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➪ ![\sf y = 100 - 78](https://tex.z-dn.net/?f=%5Csf%20y%20%3D%20100%20-%2078)
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★ ![\large{\bold\red{y = 22}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cbold%5Cred%7By%20%3D%2022%7D%7D)
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Therefore, the numbers are 78 and 22.
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The larger number is 78.