[tex]\pink{\bigstar}[/tex] The larger number is [tex]\large\leadsto\boxed{\tt\purple{78}}[/tex]
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Let the two numbers be 'x' and 'y' respectively.
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According to the question:-
✯ Sum of two numbers is 100.
➪ [tex]\sf x + y = 100 \dashrightarrow\bold\red{[equation \: 1]}[/tex]
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Also,
✯ Difference between the numbers is 56.
➪ [tex]\sf x - y = 100 \dashrightarrow\bold\red{[equation \: 2]}[/tex]
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• Adding equation [1] and equation [2]:-
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➪ [tex]\sf (x + y) + (x - y) = 100 + 56[/tex]
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➪ [tex]\sf x + y + x - y = 156[/tex]
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➪ [tex]\sf 2x = 156[/tex]
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➪ [tex]\sf x = \dfrac{156}{2}[/tex]
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★ [tex]\large{\bold\red{x = 78}}[/tex]
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• Substituting the value of x in equation [1]:-
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➪ [tex]\sf x + y = 100[/tex]
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➪ [tex]\sf 78 + y = 100[/tex]
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➪ [tex]\sf y = 100 - 78[/tex]
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★ [tex]\large{\bold\red{y = 22}}[/tex]
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Therefore, the numbers are 78 and 22.
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The larger number is 78.
Answer:
[tex]here \: given \: that \: sum = 100 \\ diffrence = 56 \\ take \: the \:large \: number = x \\another = y \\ thenx - y = 56 \\ y = x - 56 \\ here \: x + y = 100 \\ x + x - 56 = 100 \\ 2x - 56 = 100 \\ 2x = 156 \\ x = \frac{156}{2} \\ x = 78 \\ large \: number \: = 78 \\ thank \: you[/tex]
