nine more than thrice a smaller numberis twice the bigger number is 26more than twice the smaller number.then what are the numbers?(write the smallest number be

Question

nine more than thrice a smaller number is twice the bigger number is 26 more than twice the smaller number.then what are the numbers?(write the smallest number before the bigger number

Answer 1

The question isn't clear but it will be the same process if I've interpreted it incorrectly. 

 

Let's say the smaller number is x₁ and the larger number is x₂. 

 

The smaller number is 3 times larger and nine more than 2 times the larger number. We can write this as an equation by saying,

 

9+3x₁=2x₂ ...(1)

 

We have two unknowns and one equation so we need an additional equation to solve for both unknowns. 

 

The bigger number is 26 more than 2 times the smaller number,

 

x₂+26=2x₁ ...(2)

 

We have a system of equations with two equations and two unknowns, we can use substitution to solve for one unknown. 

 

x₂+26 = 2x₁-->x₁= (x₂+26)/2

 

Now plug this into equation (1) for x₁

 

9+3[(x₂+26)/2] = 2x₂ ---> 9+(3/2)x₂+39=2x₂

 

48 = (1/2)x₂ ---> x₂ = 96

 

Now plug 96 into either equation (1) or (2) for x₂ to solve for x₁ 

 

Using equation (1), 

 

9+3x₁=2*96 ---> x₁ = (192-9)/3 = 61

 

So the smaller number is 61 and the larger number is 96