A string of decorative lights is 25 feet long. The first light on the string is 16 inches from the plug. The lights on the strin
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Answer:
- penny object: 5
- quarter object: 10
- circle object: 20
Step-by-step explanation:
The first thing to realize is that the penny object is <em>not</em> worth 1, and the quarter object is <em>not</em> worth 25. Once you realize <em>the values are not what they seem</em>, 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.
