If x% of y is 100 and y% of z is 200, find the relation between x and z.
2023
If x% of y is 100 and y% of z is 200, find the relation between x and z.
Answer: B. z = 2x — CONCEPTA percentage statement a% of b = c translates to ab/100 = c. When two percentage equations share a factor, dividing one equation by the other cancels…
- A.
\(z=\frac{x}{2}\)
- B.
z = 2x
- C.
z = 4x
- D.
More than one of the above
- E.
None of the above
Attempted by 3 students.
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Correct answer: B
CONCEPT
A percentage statement a% of b = c translates to ab/100 = c.
When two percentage equations share a factor, dividing one equation by the other cancels that common factor and reveals the relation between the remaining variables.
APPLICATION
From x% of y = 100, xy/100 = 100, so xy = 10,000.
From y% of z = 200, yz/100 = 200, so yz = 20,000.
Divide the second product by the first: yz/xy = 20,000/10,000. Since y is nonzero, cancel y to obtain z/x = 2, and therefore z = 2x.
CROSS-CHECK
For z = 2x, yz = 2xy = 20,000. Thus y% of z is 200 while x% of y is 100, so both original conditions hold.
Therefore, z = 2x.