The ratio of Sylvia's age to Bob's age is 3 to 7. The ratio of Sylvia's age to Joe's is 4 to 9. The ratio of Bob's age to Joe's is:
A. 28 to 27
B. 7 to 9
C. 27 to 18
D. 10 to 13
S:J = 4:9
S:B = 3:7
multiply both ratios to get 12
S:J = 12:27
S:B = 12:28
B:J = 28:27
To find the ratio of Bob's age to Joe's age, we need to use the information given.
Let's assign variables to represent Sylvia's age, Bob's age, and Joe's age. Let's say Sylvia's age is represented by S, Bob's age is represented by B, and Joe's age is represented by J.
Given the ratios:
- Sylvia's age to Bob's age is 3 to 7, which can be written as S/B = 3/7.
- Sylvia's age to Joe's age is 4 to 9, which can be written as S/J = 4/9.
To find the ratio of Bob's age to Joe's age, we need to eliminate the variables Sylvia's age and solve for B/J.
To eliminate Sylvia's age, we need to manipulate the equations. Multiply both sides of the first equation (S/B = 3/7) by J, and multiply both sides of the second equation (S/J = 4/9) by B:
(S/B) * J = (3/7) * J
(S/J) * B = (4/9) * B
This gives us:
Solve for B/J:
(B * J) / B = (3J/7)
(B * J) / J = (4B/9)
Simplifying these equations:
J = (3J/7)
B = (4B/9)
To eliminate the variables J and B, we can cross-multiply:
7J = 3J
9B = 4B
Now, divide both sides of the equations by J and B to solve for the ratios:
7J/3J = 1
9B/4B = 1
Therefore, the ratio of Bob's age to Joe's age is 1 to 1, which can be written as 1:1.
So, the correct option is not provided in the answer choices.
Let's solve the problem step-by-step:
The ratio of Sylvia's age to Bob's age is 3 to 7.
Let's assume Sylvia's age as x, and Bob's age as y.
So, we can write the equation as:
x/y = 3/7
The ratio of Sylvia's age to Joe's age is 4 to 9.
Let's assume Joe's age as z.
So, we can write the equation as:
x/z = 4/9
To find the ratio of Bob's age to Joe's age, we need to find the ratio of y/x.
To do that, we can rearrange the first equation:
x/y = 3/7
Cross-multiply:
7x = 3y
Divide both sides by 3:
7x/3 = y
Now, substitute this value of y in the second equation:
x/z = 4/9
Substitute y = 7x/3 in the second equation:
x/z = 4/9
7x/3 / z = 4/9
Cross-multiply:
7x * 9 = 4 * 3z
63x = 12z
Divide both sides by 3:
21x = 4z
Now, to find the ratio of Bob's age to Joe's age, divide both sides by x:
21x/x = 4z/x
21 = 4z/x
So, the ratio of Bob's age to Joe's age is 21 to x.
Since we don't have the value of x, we cannot determine the exact ratio of Bob's age to Joe's age. Therefore, none of the options provided (A. 28 to 27, B. 7 to 9, C. 27 to 18, D. 10 to 13) is correct.