Want to go to the trip

Number Theory Level 4

Three classes $A,B$ and $C$ decided to go on trip and each class organized a fundraising event, and they raised $\$1059$ , $\$1417$ and $\$2312$ respectively. After deduction of trip fee for each student, each class was returned an amount of $\$N$ , where $N$ is an integer.

What is the trip fee for each student?

Note: The trip fee is greater than $1\$$ .

The answer is 179.

1 solution

Abdeslem Smahi
Aug 18, 2015

We have :

$1059=q_1.t+N$

$1417=q_2.t+N$

$2312=q_3.t+N$

so that lead to:

$t(q_2-q_1)=1417-1059=358$

$t(q_3-q_2)=2312-1417=895$

$t(q_3-q_1)=1417-1059=1253$

so $t|358, t|895,t|1253 \implies t|(358,895,1253) \implies t|179$

so the trips fee is $179$

I don't fully understand your solution

Nehemiah Osei - 5 years, 8 months ago

Want to go to the trip

The answer is 179.

1 solution

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