James had some money in his wallet with values between $60 to $150. If he buys the maximum number of water bottles he can afford at $7 each, he will have $1 left. If he buys the maximum number of towels at $9 each, he would have $3 left. What is the actual amount James had?
7 x (n + 1) + 1 --> 9 x n + 3
2 n --> 7 + 1 - 3 = 5 X
7 x (n + 2) + 1 --> 9 x n + 3
2 n --> 14 + 1 - 3 = 12
n --> 12/2 = 6
9 x 6 + 3 = 57 Answer not within the range
9 x 7 = 63 9 units of 7 --> 7 parts of 9
63 + 57 = $120 So need to add multiple of 63 (7 x 9 or 9 x 7)
It was $120.
Alternative method
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[][][][][][][][ 7+1 ] [7][7][7][7][7][7][7][7][7]
[][][][][][][][][][3] [ 9 ][ 9 ][9 ][9 ][ 9 ][9 ][9 ]
2 u --> 7 + 1 - 3 = 5 X
[][][][][][][][7 x 2 + 1]
[][][][][][][][][][ 3 ]
2 u --> 7 x 2 + 1 - 3 = 12
1 u --> 12/2 = 6
6 x 9 + 3 = 57 Not within range
7 x 9 = 63
63 + 57 = $120
It was $120.
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