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CEMC Gauss (Grade 8), 2013

Algebra Difficulty 1.3 Junior Find the answer Canada

Mathy Manuel’s autograph was once worth $100. The autograph then dropped 30% in value. If it then increased by 40%, its value would be

Pick one

Solution

Since Ahmed stops to talk with Kee one quarter of the way to the store, then the remaining distance to the store is $1-\frac{1}{4}=\frac{3}{4}$ of the total distance.

Since $\frac{3}{4}=3 \times \frac{1}{4}$ , then the distance that Ahmed travelled from Kee to the store is 3 times the distance that Ahmed travelled from the start to reach Kee.
That is, 12 km is 3 times the distance between the start and Kee. So the distance between the start and Kee is $\frac{12}{3}=4$ km. Therefore, the total distance travelled by Ahmed is $4+12$ or 16 km.

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