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jeka94
3 years ago
15

What other compatible numbers could you use for 428 and 286

Mathematics
1 answer:
kaheart [24]3 years ago
4 0
How about raising 286 up by 14 to 300 and compensating by lowering 428 by the same 14 Since I know that 14 + 14 is 28  then 28-14 is 14
So 428 - 14 = 414
So now I have 414 + 300 which I can do mentally - the answer is 714 and is also the answer to the original problem 428 + 286

Compensation works very well - bring one number up or down to a rounded number and compensate by doing the opposite to the other  - instead of 199 + 457 - try 200 + 456
Same answer and because one of the numbers is nicely rounded, it is easy to add the other. 

One more:  207 + 182  becomes 200 + 189 =389   I lowered one by 7 and raised the other one by the same 7.

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9514 1404 393

Answer:

  (x, y) = (34/5, -4/5) = (6.8, -0.8)

Step-by-step explanation:

Subtract the first equation from the second to eliminate x.

  \left(\dfrac{x}{3}-\dfrac{y}{2}\right)-\left(\dfrac{x-5}{3}+\dfrac{y+2}{3}\right)=\left(\dfrac{8}{3}\right)-(1)\\\\y\left(-\dfrac{1}{2}-\dfrac{1}{3}\right)+\left(\dfrac{5}{3}-\dfrac{2}{3}\right)=\dfrac{5}{3} \qquad\text{partially simplify}\\\\-\dfrac{5}{6}y=\dfrac{2}{3} \qquad\text{subtract 1}\\\\y=-\dfrac{4}{5} \qquad\text{multiply by $-\dfrac{6}{5}$}

Substituting for y in the second equation, we can find x.

  \dfrac{x}{3}-\dfrac{1}{2}\left(-\dfrac{4}{5}\right)=\dfrac{8}{3}\\\\5x +6=40 \qquad\text{multiply by 15}\\\\5x=34\qquad\text{subtract 6}\\\\x=\dfrac{34}{5}

The solution is (x, y) = (34/5, -4/5) = (6.8, -0.8).

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