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Combinatorics Difficulty 3.8 AMC 10/12 Find the answer Canada

Three spinners are shown. The spinners are used to determine the hundreds, tens and ones digits of a three-digit number.

How many possible three-digit numbers that can be formed in this way are divisible by 6?

Pick one

Solution

Celyna spent $5.00 on candy A and$ 7.00 on candy B, or 12.00 in total. The average price of all the candy that she purchased was

Figure for this problem 1.50 per 100 grams.

This means that if Celyna bought 100 grams of candy, she would have spent 1.50. If she bought 200 grams of candy, she would have spent

Figure for this problem $2\times\$1.50=\$3.00$ . How many grams of candy would Celyna need to buy to spend

Figure for this problem 12.00?

Since $8\times\$1.50=\$12.00$ (or $\$12.00\div\$1.50=8$ ), then she would need to buy a total of 800 grams of candy. Celyna bought 300 grams of candy A, and so she must have purchased $800-300=500$ grams of candy B. The value of $x$ is 500.

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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.