Question

12)
scale factor from a to b = 8 : 9
14)
scale factor from a to b = 3 : 4
16)
scale factor from a to b = 4 : 5

Explanation:

Step1: Set up proportion for Q12

$\frac{5x - 13}{81} = \frac{8}{9}$

Step2: Solve for x in Q12

Multiply both sides by 81: $5x - 13 = 81 \times \frac{8}{9} = 72$
Add 13 to both sides: $5x = 72 + 13 = 85$
Divide by 5: $x = \frac{85}{5} = 17$

Step3: Set up proportion for Q14

$\frac{9}{-x + 23} = \frac{3}{4}$

Step4: Solve for x in Q14

Cross multiply: $9 \times 4 = 3(-x + 23)$
Simplify: $36 = -3x + 69$
Subtract 69: $36 - 69 = -3x$
Simplify: $-33 = -3x$
Divide by -3: $x = 11$

Step5: Set up proportion for Q16

$\frac{24}{3x - 9} = \frac{4}{5}$

Step6: Solve for x in Q16

Cross multiply: $24 \times 5 = 4(3x - 9)$
Simplify: $120 = 12x - 36$
Add 36: $120 + 36 = 12x$
Simplify: $156 = 12x$
Divide by 12: $x = \frac{156}{12} = 13$

Answer:

1. $x = 17$
2. $x = 11$
3. $x = 13$