Arithmetic › Integers and signed numbers

Adding signed numbers

Solve the first problem 17 problems

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1. Sum of three numbers from pairwise sums ●○○○○ 10 ptsThree numbers are added two at a time, and the three sums are 29, 46, and 53. Find the sum of all three numbers.
2. Three numbers from pairwise sums ●○○○○ 10 ptsLet the three numbers be $x$, $y$ and $z$ with $x+y=10$, $y+z=19$ and $x+z=21$. Find $x$, $y$ and $z$.
3. Sum of three integers ●○○○○ 10 ptsFind the sum of $-312$, $39$ and $192$.
4. Smallest non-negative signed sum ●●○○○ 20 ptsInsert $+$ or $-$ signs between the numbers $1, 2, 3, \ldots, 1989$, so that the sum is $\pm1\pm2\pm3\cdots\pm1989$ with the first number taken as $+$. What is the smallest non-negative value that the sum can take?
5. Sum of variables in a month-length equation ●●●○○ 50 ptsLet $x$, $y$, $z$ be natural numbers satisfying $29x+30y+31z=366$. Find $x+y+z$.

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