To solve for the missing values in the given proportion, we can use the concept of equivalent ratios. Let's denote the missing values by \( a, b, c, \) and \( d \) respectively.
Given proportion:
\[ \frac{4}{5} = \frac{8}{a} = \frac{b}{15} = \frac{c}{20} = \frac{20}{d} \]
First, solve for \( a \) using the ratio \( \frac{4}{5} = \frac{8}{a} \):
\[ \frac{4}{5} = \frac{8}{a} \]
\[ 4a = 5 \cdot 8 \]
\[ 4a = 40 \]
\[ a = 10 \]
So, \( a = 10 \). Therefore:
\[ \frac{4}{5} = \frac{8}{10} \]
Next, solve for \( b \) using the ratio \( \frac{4}{5} = \frac{b}{15} \):
\[ \frac{4}{5} = \frac{b}{15} \]
\[ 4 \cdot 15 = 5b \]
\[ 60 = 5b \]
\[ b = 12 \]
So, \( b = 12 \). Therefore:
\[ \frac{4}{5} = \frac{12}{15} \]
Next, solve for \( c \) using the ratio \( \frac{4}{5} = \frac{c}{20} \):
\[ \frac{4}{5} = \frac{c}{20} \]
\[ 4 \cdot 20 = 5c \]
\[ 80 = 5c \]
\[ c = 16 \]
So, \( c = 16 \). Therefore:
\[ \frac{4}{5} = \frac{16}{20} \]
Finally, solve for \( d \) using the ratio \( \frac{4}{5} = \frac{20}{d} \):
\[ \frac{4}{5} = \frac{20}{d} \]
\[ 4d = 5 \cdot 20 \]
\[ 4d = 100 \]
\[ d = 25 \]
So, \( d = 25 \). Therefore:
\[ \frac{4}{5} = \frac{20}{25} \]
So the complete proportion with the missing values filled in is:
\[ \frac{4}{5} = \frac{8}{10} = \frac{12}{15} = \frac{16}{20} = \frac{20}{25} \]
4/5 = 8/? = ?/15 = ?/20 = 20/?
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