Let’s assume that each diagram represents a letter. So,
The circle represents the letter “c”,
The square represents the letter “s”,
The triangle represents the letter “t”,
And the hexagon represents the letter “h”.
Now, we write down all of the equations that are given to us in the table.
So,
2s +2t = 28,
2s + 2h = 30,
3c + t = 18,
3c + s = 20,
2c + s + t = 22,
2c + s + t =23,
3s + t = 30,
and finally,
2c + h + t = ?
The first equations that will be solved simultaneously are,
3c + s = 20
And, 3c + t = 18.
As 20 is larger than 18, we subtract 3c + t = 18 from 3c + s = 20.
3c + s = 20
(-) 3c + t = 18
s – t = 2
Now, we need to simplify the equation, 2s + 2t = 28.
2s + 2t = 28, if we factorize this equation we get,
2(s + t) = 28, so then we have,
s + t = 28/2, so,
s + t = 14.
Now we have two different equations which both have the same two variables in them.
They are,
s + t =14, and
s – t = 2.
So if we solve these simultaneously,
s + t = 14,
(+) s – t = 2
2s = 16
s = 8
Now we now that the square is worth 8, we can also find what the triangle is worth by substituting it with the equation, s + t = 14.
So we find the triangle is worth 6.
Now,
3c + t = 18
3c + 6 = 18
3c = 12
c = 4.
The circle is worth 4.
To find the worth of the hexagon, we substitute 8 with the s in the equation,
2h + 2s = 30
2h + 16 = 30
2h = 14
h = 7
Now we know that the hexagon is worth.
So,
Square = 8
Circle = 4
Triangle = 6
Hexagon = 7.
So now we substitute all these with the equation,
2c + h + t = ?
8 + 7 +6 = ?
so the ‘?’ is worth 21.