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satela [25.4K]
3 years ago
5

Rajiv is building a bookcase a shelf on the bookcase can hold up to 95 pounds of books write an inequality to represent the situ

ation where b represent the weight of books on the shelf
Mathematics
1 answer:
mihalych1998 [28]3 years ago
5 0
The first thing we must do in this type of problem is first to name the variables that we are going to use to write the inequality.
 We have then:
 b = the weight of books on the shelf.
 The inequality is:
 b <= 95
 answer:
 An inequality to represent the situation is
 b <= 95
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Question 4: 11 p The sum of the digits of a two-digit number is 14. When the digits are reversed the new number is 36 less than
svetoff [14.1K]

Answer:

  95

Step-by-step explanation:

Let x represent the ones digit. The tens digit will be higher, because reversing the digits results in a lower number. Its value is (14 -x). The given relation is ...

  (10(14-x) +x) -(10x +(14 -x)) = 36 . . . . reversing the digits gives 36 less

  140 -9x -9x -14 = 36 . . . . eliminate parentheses

  90 = 18x . . . . . . . . add 18x-36

  5 = x . . . . . . ones digit

  14-5 = 9 . . . tens digit

The original number is 95.

__

<em>Check</em>

  95 -59 = 36

_____

<em>Additional comment</em>

The difference in value when the digits of a 2-digit number are reversed is always 9 times the difference in the digits. This means the difference in the digits is 36/9 = 4. Since the sum of digits is 14, the two digits are (14+4)/2 = 9 and (14-4)/2 = 5. 95 is the number of interest.

The solutions to a "sum and difference" problem are half the sum and half the difference of the given sum and difference. That is how we know the larger digit is (1/2)(14 + 4), for example.

We worked this "the hard way" using the above equation. It can actually be worked in your head if you're familiar with these generic solutions.

4 0
3 years ago
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