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 $840-1-2+\tfrac1{420}=837\tfrac1{420}$ .

1997 PMWC (Problems)
Preceded by First question	Followed by Problem I2
I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10

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1997 PMWC Problems/Problem I1

Contents

Problem

Solution 1

Solution 2

See Also