Question

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

Answer 1

`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 = (156)/(2) \\ x = 78 \\ large \: number \: = 78 \\ thank \: you`

Answer 2

Answer:-

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Given:-

• Sum of two numbers is 100.

• Difference between the numbers is 56.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• To Find:-

• The larger number = ?

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Solution:-

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

According to the question:-

✯ Sum of two numbers is 100.

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Also,

✯ Difference between the numbers is 56.

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪
`\sf (x + y) + (x - y) = 100 + 56`

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪
`\sf x + y + x - y = 156`

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪
`\sf 2x = 156`

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪
`\sf x = (156)/(2)`

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★
`\large{\bold\red{x = 78}}`

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪
`\sf x + y = 100`

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪
`\sf 78 + y = 100`

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪
`\sf y = 100 - 78`

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★
`\large{\bold\red{y = 22}}`

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore, the numbers are 78 and 22.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

The larger number is 78.