In a 3 digit number, the tens digit equals to the sum of the hundreds digit and the units digit. The hundreds digit of this number is 3 more than the units digit. If the digits were reserved, the new number is 11 less than half of the original number. Find the original number.

The original number is 572.

Step-by-step explanation:

Let the 3 digit number by xyz.

Where x is the hundreds digit, y is the tens digit and z is the units digit.

Hence, the digit is (100x + 10y + z).

From the question, the tens digit equals to the sum of the hundreds digit and the units digit.

That is,

y = x + z (1)

Also, from the question, the hundreds digit of this number is 3 more than the units digit.

That is,

x = z + 3 (2)

Also, from the question, If the digits were reserved, the new number is 11 less than half of the original number

If the digit were reversed, that is xyz becomes zyx. Then, the new number is (100z + 10y + x).

the new number is 11 less than half of the original number

That is,

(100z + 10y + x) + 11 = 1/2(100x + 10y + z)

This becomes

200z + 20y + 2x + 22 = 100x + 10y + z

200z - z +20y -10y +2x - 100x = -22

199z + 10y -98x = -22 (3)

Solving the equations simultaneously,

Put the value of x in equation (2) into equation (1)

x = z + 3 (2)

y = x + z (1)

That is,

y = (z+3) + z

y = 2z + 3 (4)

Put the value of y in equation (4) into equation (3)

199z + 10y -98x = -22

199z + 10(2z +3) -98x = -22

199z + 20z + 30 -98x = -22

219z -98x = -22-30

219z -98x = -52 (6)

Put the value of x in equation (2) into equation (6)

219z -98(z+3) = -52

219z -98z -294 = -52

121z = -52 + 294

121z= 242

z = 242/121

∴ z = 2

Put the value of z into equation (2)

x = z + 3

x = 2 + 3

∴ x = 5

Put the values of z and x into equation (1)

y = x + z

y = 5 + 2

∴ y = 7

Hence, x = 5, y = 7 and z = 2.

Recall that the original number is 100x + 10y + z.

100x + 10y + z = 100(5) + 10(7) +2 = 500 + 70 + 2 = 572

Hence, the original number is 572.

300

step-by-step explanation:

28-600w < 300

28-600w > 300

600-28w < 300

600-28w > 300

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)