Mo2men wrote:At an amusement park, tom bought a number of red tokens and green tokens. Each red token costs $0.09, and each green token costs $0.14. If Tom spent a total of exactly $2.06, how many token in total did Tom buy?
A. 16
B. 17
C. 18
D. 19
E. 20
One approach:
9r +
14g =
206.
Since the two values in blue are even, the term in red must also be even, implying that the term in red is a MULTIPLE OF 18.
Thus, the equation can be rephrased as follows:
9(2x) + 14g = 206
9x + 7g = 103
7g = 103 - 9x
g = (103 - 9x)/7.
Since g is a INTEGER, 103-9x must be a MULTIPLE OF 7.
Keep subtracting 9 from 103 until a multiple of 7 is yielded:
103-9 = 94
94-9 = 85
85-9 = 76
76-9 = 67
67-9 = 58
58-9 =
49.
The value in green is a multiple of 7.
Implication:
103-9x = 49, with the result that g = 49/7 = 7.
Substituting g=7 into 9r-14g = 206, we get:
9r - 14(7) = 206
9r - 98 = 206
9r = 108
r = 12.
Thus, r+g = 12+7 = 19.
The correct answer is
D.
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