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Ronch [10]
3 years ago
13

Directions: Using the digits 1 to 9, at most one time each, fill in the boxes to find the largest or smallest possible values fo

r the sum of X and Y.

Mathematics
2 answers:
12345 [234]3 years ago
8 0

9514 1404 393

Answer:

  smallest: 8x -3 = 4; 1y +9 = 2. total = -49/8

  largest: 1x -9 = 8; 2y +3 = 7. total = 19

Step-by-step explanation:

If we use variables to represent the box contents, we can write ...

  • ax -b = c
  • dy +e = f

Then the values of x and y are ...

  x = (c +b)/a

  y = (f -e)/d

For positive integer values of the variables, x will always be positive, and y may or may not be negative.

<h3>Smallest sum</h3>

For the sum to be the smallest, we must have x be as small as possible and the ratio (f-e)/d be as negative as possible.

x will be small for large 'a' and for (c+b) small. For y to be as negative as possible, we want 'd' and 'f' small and 'e' large. Best results are obtained for

  • 8x -3 = 4   ⇒   x = 7/8
  • 1y +9 = 2   ⇒   y = -7

For these coefficients, the sum is -6 1/8 = -49/8.

(note that the values of 'b' and 'c' can be swapped with no net effect)

<h3>Largest sum</h3>

For the sum to be the largest, we must have x as large as possible: (b+c) large and 'a' small. At the same time we must have y be positive and as large as possible: (f-e) positive and large, 'd' small. Best results are obtained for

  • 1x -9 = 8  ⇒   x = 17
  • 2y +3 = 7   ⇒   y = 2

For these coefficients, the sum is 19. Again, 'b' and 'c' can be swapped with no effect.

_____

<em>Additional comment</em>

These extreme values are verified by examination of the 60,480 possible permutations of the coefficients.

eimsori [14]3 years ago
6 0

Answer:

Smallest: <u>8</u><u>x</u><u>-</u><u>3</u><u>=</u><u>4</u><u>;</u><u> </u><u>1</u><u>y</u><u>+</u><u>9</u><u>=</u><u>2</u><u>.</u><u> </u><u> </u><u>total</u><u>=</u><u> </u><u>-</u><u>4</u><u>9</u><u>/</u><u>8</u>

Largest: <u> </u><u>1</u><u>x</u><u>-</u><u>9</u><u>=</u><u>8</u><u>;</u><u> </u><u>2</u><u>y</u><u>+</u><u>3</u><u>=</u><u> </u><u>7</u><u>.</u><u> </u><u> </u><u>total</u><u>=</u><u> </u><u>1</u><u>9</u>

Step-by-step explanation:

<h3>#CARRYONLEARNING</h3>

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<h3>Step-by-step explanation:</h3>

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