SOLUTION: Two girls are practising their arithmetic. They take two different numbers. The first girl finds half the sum of the numbers and divides her answer by 3. The second girl, multiplie

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Question 945407: Two girls are practising their arithmetic. They take two different numbers. The first girl finds half the sum of the numbers and divides her answer by 3. The second girl, multiplies the sum of the numbers by 3 and divides her answer by 2. They then divide the first girl's answer by the second girl's answer This should give an answer of



a. 1/3 b. 1/9 c. 2/3 d. There is not enough information to tell
Found 3 solutions by Theo, josmiceli, MathLover1:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the answer will be 1/9.

you can use numbers or you can use letters to solve his.

since the same 2 numbers that are different from each other are used by both girls, their sum will be the same.

we'll let the letter x represent the sum of the 2 numbers.

the first girl divides that sum by 2 and then divides the result by 3.

the first girl's number becomes (x/2) / 3 which is the same as x/6.

the second girl multiplies that sum by 3 and then divides the result by 2.

the second girl's number becomes (3 * x) / 2 which is the same as 3x/2.

they then divide the first girl's number by the second girl's number to get:

x/6 divided by 3x/2 which is the same as:

x/6 * 2/(3x) which is the same as:

(x*2) / (6*3*x)

the x in the numerator and the denominator cancels out.

you are left with:

2 / 18 which simplifies to 1/9.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 1st girl's number = +a+
Let the 2nd girl's number = +b+
-------------------------------
(1) +%28+%28+a+%2B+b+%29+%2F+2+%29+%2F+3+
(2) +%28+3%2A%28+a+%2B+b+%29+%29+%2F+2+
-------------------------
(1) +%28+a+%2B+b+%29+%2F+6+
and
(2) +%28+3%2F2+%29%2A%28+a+%2B+b+%29+
-----------------------
(1) divided by (2) is:
+%28+%28+a+%2B+b+%29+%2F+6+%29+%2F+%28+%28+3%2F2+%29%2A%28+a+%2B+b+%29+%29+
Divide top and bottom by +a+%2B+b+
+%28+1%2F6+%29+%2F+%28+3%2F2+%29+
+%28+1%2F6+%29%2A%28+2%2F3+%29+
+2%2F18+=+1%2F9+
The answer is (b)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
They take two different numbers,x and y.
The first girl finds half the sum of the numbers and divides her answer by 3.
%28%28x%2By%29%2F2%29%2F3

%28%28x%2By%29%2F2%29%2F%283%2F1%29

%28x%2By%29%2F6
The second girl, multiplies the sum of the numbers by 3 and divides her answer by 2.

3%28x%2By%29%2F2
They then divide the first girl's answer by the second girl's answer

%28%28x%2By%29%2F6%29%2F%283%28x%2By%29%2F2%29

%282%28x%2By%29%29%2F%286%2A3%28x%2By%29%29

%28cross%282%291cross%28%28x%2By%29%29%29%2F%28cross%286%293%2A3cross%28%28x%2By%29%29%29

1%2F9-> your answer