The pattern increases by 2 squares at every stage. The next three stages after Stage 4 will have 9, 11 and 13 squares. Therefore, the sequence up to Stage 7 is 1, 3, 5, 7, 9, 11, 13.
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Let the width be x cm. Then the length is 2x plus 3 cm. Using the perimeter formula gives 2 multiplied by length plus width equals 24. Solving gives width 3 cm and length 9 cm.
Let the number of five-rupee coins be x. Then the number of two-rupee coins is 3x. Their total value is 88 rupees. Solving the equation gives x equal to 8. Therefore, Ruby has 24 two-rupee coins and 8 five-rupee coins.
Let the shorter piece be x feet. Then the longer piece is 4x feet. Their total length is 300 feet. Solving 5x equals 300 gives x equal to 60. Therefore, the two pieces are 60 feet and 240 feet.
Let the integers be 2x and 5x because their ratio is 2:5. Their difference is 63. Therefore, 5x minus 2x equals 63. Solving gives x equal to 21. Hence, the integers are 42 and 105.