Answer:
- penny object: 5
- quarter object: 10
- circle object: 20
Explanation:
The first thing to realize is that the penny object is not worth 1, and the quarter object is not worth 25. Once you realize the values are not what they seem, but are consistent throughout, it becomes a different problem than it first appears to be.
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Let p, q, c represent the values of the penny object, the quarter object, and the circle object, respectively. The trick is to find 3 independent equations describing their values.
The middle two rows of the matrix shown give rise to the equations ...
2p +c +q = 40
p +2c +q = 55
The leftmost column adds a third independent equation ...
p + c + 2q = 45
We can subtract the last equation from the middle one.
(p +2c +q) -(p +c +2q) = 55 -45
c - q = 10 . . . . . simplify . . . [eq4]
And we can subtract the first equation from twice the last one.
2(p +c +2q) -(2p +c +q) = 2(45) -40
c +3q = 50 . . . . simplify . . . [eq5]
Subtracting eq4 from eq5 gives ...
(c +3q) -(c -q) = (50) -(10)
4q = 40 . . . . simplify
q = 10 . . . . . .divide by 4
The eq4 tells us
c = 10 + q = 10 + 10 = 20
and the third equation tells us
p = 45 - 2q - c = 45 -2·10 -20 = 5
The object values are: penny, 5; quarter, 10; circle, 20.