Question

The difference of two numbers is 54. The first number is 7 times the second number. The greatest number is​

Answer 1

Solution

Given:-

• Difference of two numbers = 54
• The first number is 7 times the second number

Find :-

• Greatest Number

Explanation

Let

• First number be = x
• Second number be = y

According to question,

Case 1.

==> x - y = 54___________(1)

Case 2.

==> x = 7y

==> x - 7y = 0___________(2)

Sub. equ(1) & equ(2)

==> -y + 7y = 54

==> 6y = 54

==> y = 54/6

==> y = 9

Keep in equ(1)

==> x - 9 = 54

==> x = 54 + 9

==> x = 63

Hence

• First number be = 63
• Second number be = 9

___________________

Answer 2

Answer:

Given:-

• The difference of two numbers is 54.
• First number is 7 times greater than second number.

To Find:-

• The greatest number?

Solution:-

• Let the smaller number be 'x'
• Let the greater number be '7x'

According to the question:-

$7x - x = 54$

Value of 'x'

$7x - x = 54 = 6x \\ \\ x = \frac{54}{6} \\ \\ \boxed{x = 9}$

Value of '7x'

$7x = x \times 7 \\ \\ 7x = 9 \times 7 \\ \\ \boxed{7x = 63}$

Hence, the greater number

is 63.

Verification:-

7x - x = 54

• x = 9
• 7x = 63

63 - 9 = 54

54 = 54

$\boxed{lhs = rhs}$

Hence, proved.