Question

the difference between two numbers is 7 six times the smaller plus the larger is 77 find the numbers

Answer 1

10 &17 are the numbers

Answer 2

$\huge\underline\mathrm{SOLUTION:-}$

AnswEr:

• $\large{\underline{\boxed{\mathfrak\blue{Two \: numbers = 10 \: \& \: 17 }}}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

Let the larger number be a & smaller number be b.

1st case:

⇒ a - b = 7

⇒ a = b + 7 .................(eq.1)

2nd case:

⇒ 6b + a = 77

Putting value of a from (eq.1):

$\sf {\: \: \: \: \:\: [\because a = b + 7]}$

⇒ 6b + b + 7 = 77

⇒ 7b + 7 = 77

⇒ 7b = 77 - 7

⇒ 7b = 70

⇒ b = 70/7

⇒ b = 10

$\therefore{\underline{\boxed{\rm{Smaller \: number = 10}}}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

Putting value of b in (eq.1):

⇒ a = 10 + 7

⇒ a = 17

$\therefore{\underline{\boxed{\rm{Larger \: number = 17}}}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$