1997 PMWC Problems/Problem I1

Problem

Evaluate $29 \frac{27}{28} \times 27\frac{14}{15}$.

Solution 1

$\frac{29 \cdot 28 + 27}{28} \cdot \frac{27 \cdot 15 + 14}{15} = \frac{839 \cdot 419}{420} = \frac{839(420 - 1)}{420} = 839 - \frac{839}{420} = 837 \tfrac{1}{420}$.

Solution 2

$(30-x)(28-y)=840-28x-30y+xy$, so for $x=\tfrac1{28},\ y=\tfrac1{15}$ the result is $840-1-2+\tfrac1{420}=837\tfrac1{420}$.

See Also

1997 PMWC (Problems)
Preceded by
First question
Followed by
Problem I2
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T: 1 2 3 4 5 6 7 8 9 10