Cricket Bats

A sporting goods store sold 64 cricket bats in one week, some for Tk. 3 and the rest for Tk. 4 each. If receipts from bat sales for the week totaled Tk. 204, what is the fewest number of Tk. 4 cricket bats that could have been sold?

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x = # of Tk. 3 bats
y = # of Tk. 4 bats

x + y = 64   {# of bats sold was 64}
3x + 4y = 204   {total for bats was 204}

-3x - 3y = -192   {multiplied top equation by -3}
3x + 4y = 204   {bottom equation stays the same}
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      y = 12   {added the two equations, eliminating the x}

x + y = 64   {first equation}
x + 12 = 64   {substituted 12, in for y, into first equation}
x = 52  {solved for x}

12  Tk. 3 bats
52  Tk. 4 bats

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