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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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5 0
3 years ago
In a certain clothing store,6 shirts and 3 ties cost $79.50 ,and 3 shirts and 2 ties cost $41. determine the cost of each shirt.
Komok [63]

Answer:

Each shirt cost $12

Step-by-step explanation:

First, we have to interpret this question and turn each to an equation, letting shirts represent the letter s and ties represent the letter t.

6 shirts and 3 ties cost $79.50 would be interpreted to 6s+3t=79.5 ,and 3 shirts and 2 ties cost $41 would be interpreted to 3s+2t=41

Hence we have two equations, and we solve them simultaneously.

6s+3t=79.5 (Equation 1)

3s+2t=41 (Equation 2)

We can either use the substitution method or the elimination method but for the sake of this question, we use the Elimination method.

6s+3t=79.5 (Equation 1)

3s+2t=41 (Equation 2)

We multiply equation 1 by 2 and we multiply equation 2 by 3, I'm prefer to eliminate the

2(6s+3t=79.5)

12s+6t=159 Equation 3

3(3s+2t=41)

9s+6t=123 Equation 4

We subtract equation 4 from equation 3.

12s+6t=159

9s+6t=123

12s-9s=3s

6t-6t=0

159-123=36

We therefore have

3s=36

Divide both sides by 3

s=36/3

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One shirt cost $12

3 0
3 years ago
Can anybody help me thank you
IceJOKER [234]
Remember that you can convert percentages to decimals by dividing them by 100.

You can convert decimals to percentages by multiplying them by 100.

Here are my answers:
11.

(a) 55% < 0.75

(b) 0.23 < 28%

(c) 74% > 0.70

(d) 1/2 < 2/3

(e) 3/4 < 7/8

(f) 3/5 > 2/11
8 0
3 years ago
Read 2 more answers
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