Sure, let's solve this step-by-step.
#### (1) Write the antecedent and consequent in the given ratio.
The given ratio is 3:8.
- The antecedent (the first term) is 3.
- The consequent (the second term) is 8.
So, the ratio is 3:8, where:
- Antecedent = 3
- Consequent = 8
#### (ii) Consider the greater number as [tex]\( x \)[/tex] and make an equation.
We are given:
- Ratio of the two numbers = 3:8
- Smaller number = 12
Let's consider the greater number to be [tex]\( x \)[/tex].
According to the given ratio, the ratio of the smaller number to the greater number should be equal to the given ratio 3:8. This translates into the equation:
[tex]\[ \frac{\text{smaller number}}{\text{greater number}} = \frac{\text{antecedent}}{\text{consequent}} \][/tex]
Substitute the values:
[tex]\[ \frac{12}{x} = \frac{3}{8} \][/tex]
#### (iii) Solve the equation to find the greater number.
To solve for [tex]\( x \)[/tex], we'll cross-multiply the terms:
[tex]\[ 12 \cdot 8 = 3 \cdot x \][/tex]
[tex]\[ 96 = 3x \][/tex]
Now, isolate [tex]\( x \)[/tex] by dividing both sides by 3:
[tex]\[ x = \frac{96}{3} \][/tex]
[tex]\[ x = 32 \][/tex]
So, the greater number is [tex]\( 32 \)[/tex].
### Summary:
1. The antecedent is 3 and the consequent is 8.
2. The equation formed is [tex]\(\frac{12}{x} = \frac{3}{8}\)[/tex].
3. The greater number is 32.
