Respuesta :
Please note that in such questions, the ":" stands for ratio which in turn stands for divide. Thus, the given expression which is:
[tex]3.8:(4c+3)=2:2\frac{2}{19}[/tex] will become:
[tex]\frac{3.8}{4c+3}= \frac{2}{2\frac{2}{19}}[/tex].....(Equation 1)
Now, we know that 3.8 can be rewritten as [tex]\frac{38}{10}[/tex]. Also, we know that the mixed fraction [tex]2\frac{2}{19}[/tex] can be re-written as:
[tex]2\frac{2}{19}=2+ \frac{2}{19}= \frac{38+2}{19}= \frac{40}{19}[/tex]
Using the above two expressions in (Equation 1) we get:
[tex]\frac{\frac{38}{10}}{4c+3}= \frac{2}{\frac{40}{19}}[/tex]
[tex]\frac{\frac{38}{10}} {4c+3}= \frac{2\times 19}{40}= \frac{38}{40}[/tex]
Cross-multiplication gives:
[tex]38(4c+3)=\frac{40\times 38}{10}[/tex]
[tex]4c+3=4[/tex][tex]4c=1[/tex]
[tex]c=\frac{1}{4}[/tex]
Or c=0.25
Thus, we may write the value of c as either the decimal 0.25 or the fraction [tex]\frac{1}{4}[/tex].
