The larger of two numbers is 7 times the smaller number. Three times the larger number is 7 more than 4 times the smaller number. Find the numbers.

Let the smaller number be x.Given, the larger number is 7 times the smaller number.So, the larger number = 7x.Given, 3 times the larger number is 7 more than 4 times the smaller number.So we can write the equation as,[tex] 3(7x) = 4(x)+7 [/tex][tex] 3(7x) = 4x+7 [/tex][tex] 21x = 4x+7 [/tex]Now we have to move 4x to the left side by subtracting 4x from both sides.[tex] 21x-4x = 4x-4x+7 [/tex][tex] 21x-4x = 7 [/tex][tex] 17x = 7 [/tex]To get x, we will divide both sides by 17. We will get,[tex] \frac{17x}{17} = \frac{7}{17} [/tex][tex] x = \frac{7}{17} [/tex]So the smaller number = [tex] \frac{7}{17} [/tex]The larger number = [tex] 7(\frac{7}{17} ) [/tex] = [tex] \frac{49}{17} [/tex]So we have got the required numbers.Smaller number = [tex] \frac{7}{17} [/tex] and larger number = [tex] \frac{49}{17} [/tex].