Question

Puzzle question, fairly easy
My answer on this is - not enough information to solve algebraically, you have to do it by trial and error. Am I wrong?
"Difference between 2 numbers is 3. 4x the smaller is divided by the larger, the quotient is 5. Find numbers"

Answer 1

Hmm *on my phone so latex won't work too well but...*

Let "x" be the smaller number
And "y" be the larger number

x-y=3
(4x)/(y) = 5

Let's solve the top equation for "x"

x=3+y

Plug that into the second equation and solve for "y"

Answer 2

I'm confused, if X and Y are givens why are they set up in that equation?
How would I "solve for X" when X is any number I pick?

Answer 3

X and Y are not given. you have the relationship between them so that for any number you pick and you know the relationship then you can find Y
Here the question is really asking what numbers were picked

Answer 4

In general, if you have two unknowns, then you need two equations
If you have two equations, you (usually) have enough info.

Answer 5

In your problem you have two equations:

"Difference between 2 numbers is 3:
x-y= 3
(we assume x is bigger than y)

4 times the smaller is divided by the larger, the quotient is 5.
the smaller is (assumed) to be y. 4 times the smaller is 4y
divided by the larger (x): 4y/x= 5

now you use algebra (if you know how)
for example, using
4y/x= 5
multiply both sides by x:
4y= 5x
now divide both sides by 4:
y= (5/4)x

use that "value" for y in the first equation
x - y = 3 becomes
\[ x-\frac{5}{4}x= 3\]