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, 2013

Algebra Difficulty 2.1 Junior Find the answer Canada

Ahmed is going to the store. One quarter of the way to the store, he stops to talk with Kee. He then continues for 12 km and reaches the store.

How many kilometres does he travel altogether?

Pick one

Solutions — 2

Solution 1

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.

Solution 2

By grouping terms using brackets as shown, $(1+1-2)+(3+5-8)+(13+21-34)$ , we can see that the result inside each set of brackets is 0.
Thus the value of $1+1-2+3+5-8+13+21-34$ is 0.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.