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Let 4-leaf clover = x, golden horseshoe = y, and St. Patrick's hat = z. This is a three-variable linear equation system. Thus, the equation is:
x + y =13 ...(1)
y - z = 6 ... (2)
x - z = 3 ... (3)
First, we need to transform the equation (2). z from the left side must be moved to the right side of the equation.
y - z = 6
y = 6 + z
y = z + 6 -> It forms a new equation, equation (4)
Second, substitute equation (4) to equation (1):
x + y = 13
x + z + 6 = 13
x + z = 13 - 6
x + z = 7 -> It forms a new equation, equation (5)
Third, eliminate z using equation (3) and (5)
x - z = 3
x + z = 7
------------- +
2x = 10
x = 10/2 = 5
x value found.
Fourth, find other unknown variable values using all defined equations.
We will pick equation (1) to find y value.
x + y = 13
5 + y = 13
y = 13 - 5 = 8
And we will pick equation (2) to find z value.
y - z = 6
8 - z = 6
z = 8 - 6 = 2
Now, substitute all values to the main problem:
x + y + z = 5 + 8 + 2 = 15
The answer is 15.
SOLVED!