Complete the following equation by the suitable method

Question

i got this linear equation two variable problems for my school. I understand the basics of the normal linear equation but this seems different instead having a pure number after the "=" they got a ration, here is the problem.

X:2Y = 5:14

(X+4) : (3Y-21) = 2:3

 

and also

 

(X+1) : (X+3) : (X+Y+4) = 2 : 3 : 6

What i've tried to do is just guess the X and Y and to solve it (took a long time and still dont find it) so as example if the X is 5 and the Y is 7, it fit the first equation but wont fit in the 2nd question.

The ":" sign is for ration, not "divided by"

Please answer how you solve and not just give the answer, because as you see im trying to learn not trying to just solve my homework.

Answer 1

The key is cross-multiplication.

 

The first two lines give (1) 7x=5y and (2) 3(x + 4) = 2(3y - 2).  Now you can solve these equations by usual methods.

 

Similarly, the third line gives (1) 3(x+1) = 2(x+3) and, say, 6(x+1) = 2(x+y+4)  (you may use the second and the third term too.)

 

D.V. G.

 

 

Answer 2

 I had an observation that was changed promptly by Scott, I agree with the solution of my colleague and that is all.