Certainly! Let's solve the given questions step-by-step.
### (i) What are the two equal ratios formed from the given terms?
The given terms are 8, 15, and 60. We can form two equal ratios from these terms:
- The ratio of the first term to the second term: [tex]\( \frac{8}{15} \)[/tex]
- The ratio of the second term to the third term: [tex]\( \frac{15}{60} \)[/tex]
### (ii) Use these two equal ratios to make an equation.
Using the equal ratios identified in part (i), we can write the equation as:
[tex]\[ \frac{8}{15} = \frac{15}{60} \][/tex]
### (iii) Solve the equation and find the first proportional.
To find the first proportional (let's denote it as [tex]\( y \)[/tex]), we use the fact that [tex]\( y \)[/tex] is related to the other terms such that:
[tex]\[ \frac{y}{8} = \frac{15}{60} \][/tex]
We know that:
[tex]\[ \frac{15}{60} = 0.25 \][/tex]
Thus, the equation becomes:
[tex]\[ \frac{y}{8} = 0.25 \][/tex]
To solve for [tex]\( y \)[/tex]:
[tex]\[ y = 0.25 \times 8 \][/tex]
[tex]\[ y = 2 \][/tex]
Therefore, the first proportional [tex]\( y \)[/tex] is [tex]\( 2 \)[/tex].
### (iv) If y were the third proportional, what would be the third term of this proportion?
If [tex]\( y \)[/tex] were the third proportional, we consider the terms as [tex]\( 8, 15, \)[/tex] and [tex]\( y \)[/tex]. The proportion would then be:
[tex]\[ \frac{8}{15} = \frac{15}{y} \][/tex]
To solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{15^2}{8} \][/tex]
[tex]\[ y = \frac{225}{8} \][/tex]
[tex]\[ y = 28.125 \][/tex]
Therefore, if [tex]\( y \)[/tex] were the third proportional, the third term of this proportion would be [tex]\( 28.125 \)[/tex].
