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Algebra Difficulty 1.4 Junior Find the answer Canada

Jim wrote the sequence of symbols $\heartsuit\,\spadesuit\,\spadesuit\,\heartsuit\,\diamondsuit\,\heartsuit\,\heartsuit\,\heartsuit\,\diamondsuit$ a total of 50 times. How many more $\heartsuit$ symbols than $\spadesuit$ symbols did he write?

Pick one

Solution

Solution 1

The sequence of symbols includes 5 $\heartsuit$ ’s and 2 $\spadesuit$ ’s.

This means that, each time the sequence is written, there are $5-2=3$ more $\heartsuit$ ’s written than $\spadesuit$ ’s.

When the sequence is written 50 times, in total there are $50 \cdot 3 = 150$ more $\heartsuit$ ’s written than $\spadesuit$ ’s.

Solution 2

The sequence of symbols includes 5 $\heartsuit$ ’s and 2 $\spadesuit$ ’s.

When the sequence is written 50 times, there will be a total of $50 \cdot 5 = 250$ $\heartsuit$ ’s written and a total of $50 \cdot 2 = 100$ $\spadesuit$ ’s written.

This means that there are $250-100 = 150$ more $\heartsuit$ ’s written than $\spadesuit$ ’s.

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