If y is 4 greater than one-fourth of x, and x ≠ 0

Solution

Given:

• y is 4 greater than one-fourth of x
• x ≠ 0

To find:

• The ratio of y to x, in terms of x

Approach and Working:
As per the given relation, we can write:

• \(y = 4 + \frac{x}{4} = \frac{16 + x}{4}\)

Therefore, the ratio of y to x is:

• \(\frac{y}{x} = \frac{16+x}{4x} = \frac{x + 16}{4x}\)

Hence, the correct answer is option C.

Answer: C

Hey Guys

Might be a silly doubt but here it is

I assumed value of y=20. therefore x=64

Now, y/x = 5/16

So even I substituted the values in option C. I don't get 5/16. Where am I going wrong?

Hey pikolo2510

Option C is \(\frac{x + 16}{4x} = \frac{64 + 16}{4*64} = \frac{80}{4*64} = \frac{5}{16}\)

Hope this clears your confusion.

Take value of X but keep it simple, so X =4..
Y =4+4*1/4=5
So y/X = 5/4

Check the values of choices by substituting X=4..
A,B and E can be eliminated as they will clearly not leave any denominator..
C =(4+16)/(4*4)=20/16=5/4
D=(4*4+1)/4

So Ans C

Silly mistake. My bad. Thanks

Posted from my mobile device

I typically prefer an algebraic approach, but we can also solve the question using the INPUT-OUTPUT approach.

Let's find values for x and y that satisfy the given information (y is 4 greater than one-fourth of x)
A nice pair of values is x = 4 and y = 5
When we use these values, the answer to our question ("what is the ratio of y to x in terms of x? ") is 5/4

In other words, when we INPUT x = 4, the OUTPUT is 4/5
So, now take each answer choice, replace x with 4 and see which one yields an OUTPUT of 5/4

A) [4² + 16(4)]/4 = 20. No good. We want an output of 5/4. ELIMINATE.
B) [4(4) + 16]/4 = 8. No good. We want an output of 5/4. ELIMINATE.
C) (4 + 16)/4(4) = 20/16 = 5/4. Great! KEEP
D) [4(4) + 1]/4 = 17/4. No good. We want an output of 5/4. ELIMINATE.
E) (4 + 16)/4 = 5. No good. We want an output of 5/4. ELIMINATE.

Answer: C