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3 years ago

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In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and m

ultiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could be

1 answer:

ASHA 777 [7]3 years ago

8 0

Answer:

4 and 13

Step-by-step explanation:

You want integer solutions to ...

15 ≤ n(n+1) ≤ 200

If we let the limits be represented by "a", then the equality is represented by ...

n² +n -a = 0

(n² +n +1/4) -a -1/4 = 0

(n +1/2)^2 = (a +1/4)

n = -1/2 + √(a +1/4)

For a=15, we have

n ≥ -1/2 + √15.25 ≈ 3.4 . . . . . minimum n is 4

For a=200, we have

n ≤ -1/2 + √200.25 ≈ 13.7 . . . maximum n is 13

The least and greatest integers on the cards are 4 and 13.

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Answer:

The greatest number of bunches of bananas that Andrea can buy is 15 and the greatest number of boxes of raspberries that Andrea can buy is 21 to maintain the ratio 7:5

Step-by-step explanation:

Let

x ---->the greatest number of boxes of raspberries that Andrea can buy

y ---->the greatest number of bunches of bananas that Andrea can buy

we know that

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$x=26.6$

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<u><em>Verify the inequality B</em></u>

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|_____|

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