Sure, let’s analyze the problem step by step.
Given:
- The ratio of two numbers is 5:2.
- The smaller number is 14.
### (i)
First, we need to determine the larger number.
Given the ratio 5:2, let:
- The antecedent (the first number) be represented by [tex]\(5x\)[/tex].
- The consequent (the second number) be represented by [tex]\(2x\)[/tex].
Since we are given that the smaller number is 14, and knowing that the smaller number in the ratio 5:2 corresponds to the consequent part:
[tex]\[ 2x = 14 \][/tex]
To find [tex]\(x\)[/tex], solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{14}{2} = 7 \][/tex]
Now to find the larger number (the antecedent):
[tex]\[ 5x = 5 \times 7 = 35 \][/tex]
So, the larger number is 35.
### (ii)
Determine which number is the antecedent or consequent:
In the ratio 5:2:
- The antecedent (first number) is 5.
- The consequent (second number) is 2.
Since the smaller number given (14) corresponds to the consequent part of the ratio 5:2, it means that 14 is the consequent.
### Summary
1. The larger number is 35.
2. The smaller number (14) is the consequent according to the given ratio.
