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PIT_PIT [208]
3 years ago
5

The units digit of a two digit number is 1 more than twice the tens digit. If the digits are reversed, the new number is 36 more

than the original number. Find the number.
Mathematics
1 answer:
Vlad1618 [11]3 years ago
6 0

Answer:

37

Step-by-step explanation:

Let the initial number be xy=10x+y.

Initial number:

Units digit = y

Tens digit = x

The units digit of a 2-digit number is 1 more than twice the tens digit, then

y=2x+1

Reversed number is yx=10y+x.

If the new number is 36 more than the original number, then

(10y+x)-(10x+y)=36

Simplify this equation:

10y+x-10x-y=36\\ \\9y-9x=36\\ \\y-x=4

Substitute y=2x+1 into the equation y-x=4:

(2x+1)-x=4\\ \\2x+1-x=4\\ \\x+1=4\\ \\x=3\\ \\y=2\cdot 3+1=7

Initial number: 37

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Find three consecutive odd integers whose sum is 495.
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The three consecutive odd integers whose sum is 495 are 163, 165, and 167.

What are consecutive numbers?

⇒ Integers that are listed in a consistent counting pattern are referred to as consecutive integers. There are no numbers missed while listing consecutive integers in a sequence, so the difference between them is always fixed. The difference between each subsequent integer is 1, for instance, can be written as -4, -3, -2, -1, 0, 1, 2, 3, and so on.

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Calculation:

We are going to take an odd number, x, write its subsequent consecutive numbers, add all of them together, then equate them to  495 to find the number. The equation for x is then resolved.

We have been given that the sum of 3 consecutive odd numbers is equal to 495.

Let the first consecutive odd integer is x.

⇒ Then the next consecutive odd integers becomes x + 2 and the next term becomes x + 2 + 2 = x + 4.

Now the sum of these three odd consecutive terms = x + x + 2 + x + 4 = 3x + 6.

According to the given,

3x + 6 = 495

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⇒ Hence, the three consecutive odd integers whose sum is 495 are 163, 165, and 167.

Learn more about consecutive numbers here: brainly.com/question/10853762

#SPJ9

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