+1310 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? Explain how you determined your answer, showing all steps along the way.
+128474 Let your current age be A .....so your age one year from now is A + 1 and one year ago was A- 1 ....and we have
For the first part, we have
(4/5)(A) > (3/4)(A + 1) multiply through by the common denominator of 4 and 5, i.e., 20
16A > 15(A + 1) simplify
16A > 15A + 15 subtract 15A from both sides
A > 15
And for the second part, we have
(4/5)A > (5/6)(A - 1) multiply through by the common denominator of 5 and 6, i.e., 30
24A > 25(A - 1) simplify
24A > 25A - 25 add 25 to both sides and subtract 24A from both sides
25 > A or, expressed another way.....
A < 25
So.....using both solutions, we have
15 < A < 25 {your possible age is greater than 15 but less than 25 }
+128474 Let your current age be A .....so your age one year from now is A + 1 and one year ago was A- 1 ....and we have
For the first part, we have
(4/5)(A) > (3/4)(A + 1) multiply through by the common denominator of 4 and 5, i.e., 20
16A > 15(A + 1) simplify
16A > 15A + 15 subtract 15A from both sides
A > 15
And for the second part, we have
(4/5)A > (5/6)(A - 1) multiply through by the common denominator of 5 and 6, i.e., 30
24A > 25(A - 1) simplify
24A > 25A - 25 add 25 to both sides and subtract 24A from both sides
25 > A or, expressed another way.....
A < 25
So.....using both solutions, we have
15 < A < 25 {your possible age is greater than 15 but less than 25 }
