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.
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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.
Let Salil’s present age be x years. Then his mother’s age is 3x years. After 5 years, their ages total 70 years. Solving gives x equal to 15. Therefore, their present ages are 15 and 45 years.
Let the smaller number be x. Then the larger number is x plus 10. Their sum is 64. Solving the equation gives x equal to 27. Therefore, the two numbers are 27 and 37.