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lord [1]
3 years ago
5

Matt is playing a game. He gains 7 points, loses 10 points, gains 2 points, and then loses 8 points. What is his final score?

Mathematics
2 answers:
Fed [463]3 years ago
8 0

you start with 7, then subtract 10 which makes -3, then add 2 which equals -1, then subtract 8 which equals -9.

saveliy_v [14]3 years ago
5 0

+7 -10+2-8 =

-3+2 -8

-1-8

-9

His final score is -9

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4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.

Start with

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x\equiv63\equiv64-1\equiv-1\equiv3\pmod4

We have 3^2\equiv9\equiv1\pmod4, so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.

x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 7, the first and last terms vanish and we're left with

x\equiv72\equiv2\pmod7

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x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 9, the first two terms vanish and we're left with

x\equiv140\equiv5\pmod9

so we don't need to make any adjustments here, and we end up with x=401.

By the Chinese remainder theorem, we find that any x such that

x\equiv401\pmod{4\cdot7\cdot9}\implies x\equiv149\pmod{252}

is a solution to this system, i.e. x=149+252n for any integer n, the smallest and positive of which is 149.

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