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Alecsey [184]
3 years ago
6

Proportion problem

"\frac{8}{9}" align="absmiddle" class="latex-formula"> = \frac{w - 2}{6}
Mathematics
2 answers:
kipiarov [429]3 years ago
6 0

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)

MrMuchimi3 years ago
3 0

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

Answer:

\\ w = 7\frac{1}{3} = 7 + \frac{1}{3} = 7.3333333333...

Step-by-step explanation:

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

Step 1: multiply each side of the equation by 6

\\ \frac{8}{9} = \frac{w-2}{6}

\\ \frac{8}{9}*6 = \frac{w-2}{6}*6

\\ \frac{8*6}{9} = \frac{6*(w-2)}{6}

\\ \frac{8*6}{9} = (w-2)*\frac{6}{6}

\\ \frac{8*6}{9} = (w-2)*1

\\ \frac{8*6}{9} = w-2

Step 2: add 2 to both sides

\\ \frac{8*6}{9} = w-2

\\ \frac{8*6}{9} + 2 = w-2+2

\\ \frac{8*6}{9} + 2 = w

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

\\ w = \frac{8*6}{9} + 2

\\ w = 8*\frac{6}{9} + 2

Simplifying the fraction \\ \frac{6}{9} = \frac{2}{3}

\\ w = 8*\frac{2}{3} + 2  

\\ w = \frac{8*2}{3} + 2  

\\ w = \frac{16}{3} + 2

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

\\ w = \frac{9 + 6 + 1}{3} + 2

\\ w = \frac{9}{3} + \frac{6}{3} + \frac{1}{3} + 2

\\ w = 3 + 2 + \frac{1}{3} + 2

\\ w = 7 + \frac{1}{3} = 7.3333333333...

Then

\\ w = 7\frac{1}{3}

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

\\ \frac{8}{9} = \frac{w-2}{6}

\\ \frac{8}{9} = \frac{7 + \frac{1}{3} -2}{6}

\\ \frac{8}{9} = \frac{5 + \frac{1}{3}}{6}

\\ \frac{8}{9} = \frac{\frac{15+1}{3}}{6}

\\ \frac{8}{9} = \frac{16}{18}

\\ \frac{8}{9} = \frac{8}{9}

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