Question

If A:B = 4:9, B:C = 3:7, and C:D = 5:2, find A : B : C : D.

• A. 20 : 45 : 105 : 42
• B. 4 : 9 : 7 : 2
• C. 12 : 27 : 63 : 18
• D. 20 : 105 : 45 : 42

Answer 1

Answer:

A. 20 : 45 : 105 : 42

To find the combined ratio $A:B:C:D$, we can equate the common terms step-by-step.

Step 1: Combine $A:B$ and $B:C$

• Given: $A:B = 4:9$

• Given: $B:C = 3:7$

To make the value of $B$ the same in both ratios, multiply the terms of $B:C$ by $3$ (so $B$ becomes $9$):

• $B:C = (3 \times 3) : (7 \times 3) = 9:21$

Now, combine $A$, $B$, and $C$:

• $A:B:C = 4:9:21$

Step 2: Combine $A:B:C$ with $C:D$

• Current ratio: $A:B:C = 4 : 9 : 21$

• Given: $C:D = 5:2$

To make the value of $C$ the same ($21$ and $5$), find the LCM of $21$ and $5$, which is $105$:

• Multiply the first ratio ($A:B:C$) by $5$:

  
  

  $A : B : C = (4 \times 5) : (9 \times 5) : (21 \times 5) = 20 : 45 : 105$

• Multiply the second ratio ($C:D$) by $21$:

  
  

  $C : D = (5 \times 21) : (2 \times 21) = 105 : 42$

Final Combined Ratio

Combining all four variables:

$A:B:C:D = 20 : 45 : 105 : 42$