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4 votes
Proportion problem



(8)/(9) =
(w - 2)/(6)

User Khrm
by
7.8k points

2 Answers

6 votes

Answer: w=66/9

Step-by-step explanation: 8/9=w-2/6

8(6)=9(w-2)

48 =9w-18

48+18=9w

66=9w

w=66/9

or w=7(3/9)

User Dpsthree
by
8.5k points
7 votes

It is assumed here that the problem targets on what the value of w is in this proportion.

Answer:


\\ w = 7(1)/(3) = 7 + (1)/(3) = 7.3333333333...

Explanation:

We need to solve the problem so the value of w equals the proportion on both sides. To achieve this, we can apply the following:

Step 1: multiply each side of the equation by 6


\\ (8)/(9) = (w-2)/(6)


\\ (8)/(9)*6 = (w-2)/(6)*6


\\ (8*6)/(9) = (6*(w-2))/(6)


\\ (8*6)/(9) = (w-2)*(6)/(6)


\\ (8*6)/(9) = (w-2)*1


\\ (8*6)/(9) = w-2

Step 2: add 2 to both sides


\\ (8*6)/(9) = w-2


\\ (8*6)/(9) + 2 = w-2+2


\\ (8*6)/(9) + 2 = w

Finally, we get an answer that can be expressed with fractions


\\ w = (8*6)/(9) + 2


\\ w = 8*(6)/(9) + 2

Simplifying the fraction
\\ (6)/(9) = (2)/(3)


\\ w = 8*(2)/(3) + 2


\\ w = (8*2)/(3) + 2


\\ w = (16)/(3) + 2

To show the result as a fraction, we can rewrite 16 as 16= 9 + 6 + 1. Then


\\ w = (9 + 6 + 1)/(3) + 2


\\ w = (9)/(3) + (6)/(3) + (1)/(3) + 2


\\ w = 3 + 2 + (1)/(3) + 2


\\ w = 7 + (1)/(3) = 7.3333333333...

Then


\\ w = 7(1)/(3)

We can prove this substituting this value in the proportion given at the beginning of the question.


\\ (8)/(9) = (w-2)/(6)


\\ (8)/(9) = (7 + (1)/(3) -2)/(6)


\\ (8)/(9) = (5 + (1)/(3))/(6)


\\ (8)/(9) = ((15+1)/(3))/(6)


\\ (8)/(9) = (16)/(18)


\\ (8)/(9) = (8)/(9)

User Chivas
by
8.3k points

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