Mathematics
Grade10
Easy

Question

The total weight of a carton box is 7 to the power of straight x over straight s end exponent and the weight of each box of chocolates is 7 to the power of x over 18 end exponent. Find the value of x if the carton box is filled with 49 boxes.

  1. 19
  2. 39 over 5
  3. 2
  4. 1 over 6

The correct answer is: 39 over 5


    Given :-
    Weight of each box of chocolates equals 7 to the power of straight x over 18 end exponent
    Weight of carton box equals 7 to the power of straight x over 8 end exponent
    Number of chocolate boxes = 49
    from unitary method :
    number of chocolate boxes=total weight of carton box / weight of one chocolate box
    So comma space 7 to the power of begin display style straight x over 8 end style end exponent over 7 to the power of begin display style straight x over 18 end style end exponent equals 49
7 to the power of straight x over 8 minus straight x over 18 end exponent equals 7 squared
7 to the power of fraction numerator 10 straight x over denominator 89 end fraction end exponent equals 7 squared
fraction numerator 10 straight x over denominator 39 end fraction equals 2
straight x equals 39 over 5

    ax/ay =ax-y  (if base are same then power are subtracted in exponential division)

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