Mr. charles cut fresh roses from his garden and gave 10 roses to his naibor. then he gave half if what was left to his neice. kept the remaining 14 rises. how many roses did he cut?

Charles cut 38 roses

Step-by-step explanation:

Mr Charles cut fresh roses from his garden and gave 10 roses to his neighbor.

The he gave half of what was left to his niece . He later kept the remaining 14 roses . The number of roses he initially cut can be computed as follows

let

Number of roses he cut = a

He gave 10 roses to his neighbor , he is left with a - 10 .

Then he gave half of what is left to his niece which is 1/2(a - 10)

Finally, he is only left with 14 roses

To know the number of rose he cut we have to minus the ones he gave out from the one he cut (a) equals to the remaining rose with him.

a - 10 - 1/2(a - 10) = 14

a - 10 - a/2 + 5 = 14

a/2 - 5 = 14

a/2 = 14 + 5

a/2 = 19

multiply both sides by 2

a  = 38

Charles cut 38 roses

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8