SOLUTION: If \[\frac{x}{y} = \frac{4}{5}, \; \frac{y}{z} = \frac{2}{5}, \;\text{and} \; \frac{z}{w} = \frac{6}{11},\] what is the value of $\dfrac{x + y + w}{z}$? Express your answer as a co

Question 1203833: If \[\frac{x}{y} = \frac{4}{5}, \; \frac{y}{z} = \frac{2}{5}, \;\text{and} \; \frac{z}{w} = \frac{6}{11},\] what is the value of $\dfrac{x + y + w}{z}$? Express your answer as a common fraction.
Found 4 solutions by ikleyn, josgarithmetic, greenestamps, math_tutor2020:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

Inappropriate format for this forum.

Print it using your keyboard to make your post readable.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Reader might try to guess that you have this:

and you have a question what is as a common fraction ?
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Type everything in your post using your keyboard. The format you use is extremely awkward.

And I won't try to guess how "dfrac" is different from "frac"....

(1)
(2)
(3)

Find

Method (perhaps not the easiest -- but the most straightforward): express y, z, and w in terms of x.

ANSWER: 383/150

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Given equations
x/y = 4/5
y/z = 2/5
z/w = 6/11

Multiply equations (1) and (2).
We multiply left hand sides (LHS) separately.
Do the same for the right hand sides (RHS)

LHS: (x/y) * (y/z) becomes x/z
RHS: (4/5)*(2/5) becomes 8/25

We conclude that x/z = 8/25
The key here is that z is the denominator.

Apply the reciprocal to both sides of equation (3) to get w/z = 11/6
We have z in the denominator as well.

---------------------

So we have:
x/z = 8/25
y/z = 2/5
w/z = 11/6
All three equations shown above have z in the denominator.

Add them up.
(x/z) + (y/z) + (w/z) = (8/25)+(2/5) + (11/6)
(x + y + w)/z = (8/25)+(10/25) + (11/6)
(x + y + w)/z = (18/25) + (11/6)
(x + y + w)/z = (18/25)*(6/6) + (11/6)*(25/25)
(x + y + w)/z = (108/150) + (275/150)
(x + y + w)/z = (108+275)/150
(x + y + w)/z = 383/150

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