Math Is Fun Forum

Wayne Hoffman

Guest

Can You Solve this One?

I came across a math question that I could not answer with any of the great resources on your site however, which I am hoping you could help me with.

The question reads:  thirty students study German, Italian or both.  The total number of students studying German is three more than the toal number of students studying Italian.  The amount of students studying one of the languages is the same as the number of students studying both languages.  How many students study Italian only?

Thank You,

Wayne H.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Can You Solve this One?

Hi Wayne H

I'd start with a Venn diagram (see below)

Then I = a + b
G = I + 3 = b + c
b = a + c
and a + b + c + d = 30

Can you solve it from here?

later edit.  My diagram is a general one for this type of problem.  Now, I've looked again at the question.  d is zero.

Thus there are four equations and four unknowns so it is just a matter of eliminating until you have only one equation and one unknown.

Recommended short route:  Use the last two to get b first; then the first two to get c in terms of a,.... then it is straight forward. 

Bob

Last edited by Bob (2011-02-10 02:42:55)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Can You Solve this One?

Question:
G = I + 3
I = ?
B = ?
Answer:
G = I + 3 + 12
I = 9
B = 9
12 + 9 + 9 = 30
Strategy: Trial/Error

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Can You Solve this One?

      *-------*
      |German |
      |   *---+---*
      | a | b | c |
      *---+---*   |
          |Italian|
          *-------*

. .

. .

.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Can You Solve this One?

hi everyone,

hi soroban

I agree with your method except I had Italian on the left so my a and c are the other way round (post #2)

hi  Shivamcoder3013

You don't need trail and error.

As a + b + c = 30 and b = a + c that means 2b = 30 so b = 15.

Then, subtracting my first two equations you get I + 3 - I = b + c - a - b => c - a = 3

So a + c = 15 and c - a = 3 => c = 9 and a = 6 => I = 21.

If you compare with sosrban'c answer you will see they are the same except we used letters a and c the other way round.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob