Answer:
350
Step-by-step explanation:
The solution to the equation can be found by multiplying by the denominator, then dividing by its coefficient.
[tex]0.22 = \dfrac{77}{x}\qquad\text{given}\\\\0.22x = 77\qquad\text{multiply by $x$}\\\\x=\dfrac{77}{0.22}=350\qquad\text{divide by the coefficient of x}[/tex]
The missing value in the fraction is 350.
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Additional comment
Here, we have rewritten the percentage as a decimal fraction. You could also rewrite it as a ratio of two integer: 22% = 22/100. Sometimes there is confusion about percentages. It can help to think of the % symbol as meaning /100:
22% = 22/100
Of course, that is "twenty-two hundredths" or 0.22.
If you just write the problem using 22/100 for 22%, then you get the proportion ...
22/100 = 77/x
22x = 7700 . . . . . "cross multiply" (multiply by 100x)
x = 7700/22 = 350 . . . . divide by the coefficient of x
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If you're paying attention, you see that the solution of this kind of equation has the appearance that the denominator variable and the left-side value are simply swapped:
[tex]0.22 = \dfrac{77}{x}\ \leftrightarrow\ x=\dfrac{77}{0.22}[/tex]
Effectively, we have multiplied both sides of the equation on the left by x/0.22. There is a property of equality that lets us do that. There is no such thing as a property of equality that says "swap with denominator." You must always pay attention to what is allowed by the properties of equality.
