To determine the ratio [tex]\( e : g \)[/tex], we need to work through the given ratios step-by-step.
We start with the two given ratios:
1. [tex]\( e : f = 3 : 4 \)[/tex]
2. [tex]\( f : g = 7 : 2 \)[/tex]
We aim to find the ratio [tex]\( e : g \)[/tex].
### Step-by-Step Solution:
1. Express [tex]\( e \)[/tex] in terms of [tex]\( f \)[/tex]:
[tex]\[
e = \frac{3}{4} f
\][/tex]
2. Express [tex]\( f \)[/tex] in terms of [tex]\( g \)[/tex]:
[tex]\[
f = \frac{7}{2} g
\][/tex]
3. Substitute the expression for [tex]\( f \)[/tex] from step 2 into the expression for [tex]\( e \)[/tex] from step 1:
[tex]\[
e = \frac{3}{4} \left( \frac{7}{2} g \right)
\][/tex]
4. Simplify the expression:
[tex]\[
e = \frac{3 \times 7}{4 \times 2} g = \frac{21}{8} g
\][/tex]
5. Write the ratio [tex]\( e : g \)[/tex] based on the previous result:
[tex]\[
e : g = \frac{21}{8} g : g
\][/tex]
Simplifying this, we get:
[tex]\[
e : g = \frac{21}{8} : 1
\][/tex]
This can also be represented as a decimal:
[tex]\[
21/8 = 2.625
\][/tex]
Thus, the ratio [tex]\( e : g \)[/tex] in its simplest fractional form is:
[tex]\[
21 : 8
\][/tex]
And in its simplest decimal form, [tex]\( e : g = 2.625 : 1 \)[/tex].
For your precise need:
Answer: [tex]\( e : g = 21 : 8 \)[/tex]
