Question

Divide 45 into four parts such that when 2 is added to the first part, 2 is
subtracted from the second part, 2 is multiplied by the third part and the
fourth part is divided by two, all result in the same number.​

Answer 1

Step-by-step explanation:

The first part is 8, the second part is 12, the third part is 5, and the fourth part is 20. The number all four operations result in is 10.

A + B + C + D = 45

A + 2 = B - 2 = 2 * C = D / 2 = E

A = E - 2

B = E + 2

C = E / 2

D = 2 * E

Therefore,

E - 2 + E + 2 + E / 2 + 2 * E = 4 * E + E / 2 = (9 * E) / 2 = 45

Therefore,

E = 10

And the rest follows.

9 * E = 90

A = 10 - 2 = 8

B = 10 + 2 = 12

C = 10 / 2 = 5

D = 10 * 2 = 20