Question

Help, please!

Four-fifths of my current age is greater than three-quarters of my age one year from now.

Four-fifths of my current age is also greater than five-sixths of my age one year ago.

Given that my age is an integer, what are all possible values for my age?

Answer 1

have you attempted this?

Answer 2

let you current age be x

then

one year from now is x + 1 so the information shows

\[\frac{4}{5} \times x > \frac{3}{4} \times (x + 1)\]

hope it helps

Answer 3

let y = my age

4/5y > 3/4y +1

-3/4y + 4/5y > 1

(4.5) -3/4y + 4/5y (4.5) > 1 * (4*5)

-15y + 16 y > 20

y > 20

Answer 4

For the second portion:

let y = my age

4/5y > 5/6y -1

-5/6y + 4/5y > -1

(6*5) -5/6y + 4/5y (6*5) > -1 (6*5)

-25y-24y > -30

-1y > -30

y < 30

Answer 5

So, all of the possible values for my age are 21,22,23,24,25,26,27,28,and 29.

Answer 6

that looks correct... your age is between 21 and 30... so

\[21 \le age \le 30\]

Answer 7

So it should read 20 < y < 30 (greater than but not equeal to 20 and less than but not equal to 30)?

Answer 8

Refer to the Mathematica attachment.

Answer 9

Thank you!

Answer 10

Your welcome.

Answer 11

thats what i got.....between 15 and 25