CEMC Fermat, 2012

Algebra Difficulty 2.3 Junior Find the answer Canada

Mary and Sally were once the same height. Since then, Sally grew 20% taller and Mary’s height increased by half as many centimetres as Sally’s height increased. Sally is now 180 cm tall. How tall, in cm, is Mary now?

Pick one

Solution

Suppose that Sally’s original height was $s$ cm.

Since Sally grew 20% taller, her new height is $1.2s$ cm.

Since Sally is now 180 cm tall, then $1.2s = 180$ or $s = \frac{180}{1.2}=150$ .

Thus, Sally grew $180 - 150 = 30$ cm.

Since Mary grew half as many centimetres as Sally grew, then Mary grew $\frac{1}{2}\cdot 30 = 15$ cm.

Since Mary and Sally were originally the same height, then Mary was originally 150 cm tall, and so is now $150+15=165$ cm tall.

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