**Quote:**

carcass wrote

At a certain school, the ratio of the number of English majors to the number of Sociology majors is 5 to 2, and the ratio of the number of Psychology majors to the number of Sociology majors is 3 to 4. If the ratio of the number of History majors to the number of English majors is 5 to 3, what is the ratio of the number of Psychology majors to the number of History majors?

(A) 25 to 3

(B) 10 to 9

(C) 9 to 50

(D) 6 to 25

(E) 3 to 10

Dokami wrote:

Please, do anybody know how to solve the problem with a ratio box?

Attachment:

ratiotable.png [ 17.87 KiB | Viewed 665 times ]
Dokami , I used one. It's quick; a little over a minute

Take it in two stages. Each discipline is represented by its first letter (English = E, etc.)

1) the ratio of the number of English majors to the number of Sociology majors is 5 to 2, and the ratio of the number of Psychology majors to the number of Sociology majors is 3 to 4.

E:S = 5:2 and P:S = 3:4 (watch order here -- you need to switch the latter in the table, Box A)

Sociology is the common term. Put it in the middle.

Box A: has split ratios because common term S has different values in each ratio:

E: S = 5:2, and S:P = 4:3

Box B: the result of multiplying the TOP ROW ONLY by 2 (so that S can = 4 in both ratios)

Box C: Combine into one row. . . .E: S: P = 10: 4: 3

2) The ratio of the number of History majors to the number of English majors is 5 to 3. What is the ratio of the number of Psychology majors to the number of History majors?

H:E=5:3 and what is P:H?

Dump Sociology now. You're not being asked about it.

Bring the numbers for (E:P) down from Box C to Box D

Box D: The common term is E. It goes in the middle.

Split the ratios again because E is not the same.

H:E = 5:

3, and E:P =

10:3

This time, to get E to have the same value, LCM of 3 and 10 is 30.

Multiply top row by 10, bottom row by 3.

Box E: the result of multiplying each row by a different factor, so E now = 30

Box F: combined results

H: E: P

50:30:9

Ratio of number of P to H? From Box F

9:50

Answer C

Hope that helps.