CEMC Cayley, 2025

Algebra Difficulty 2.4 Junior Find the answer Canada

In the diagram, a number is to be written at each of the vertices of the three pentagons. Some of the numbers have already been written.

If the sum of the numbers at the vertices of each pentagon is to be
$25$ , what is the value of $x$ ?

Pick one

Solution

We begin by labelling the missing numbers $v$ , $w$ , $y$ , and $z$ , as shown.

From the pentagon on the left, we get $4+9+5+v+w=25$ or $18+v+w=25$ , and so $v+w=7$ .

From the pentagon on the right, we get $7+3+7+y+z=25$ or $17+y+z=25$ , and so $y+z=8$ .

From the middle pentagon, we get $(v+w)+x+(y+z)=25$ or $7+x+8=25$ , and so $x=25-7-8=10$ .

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