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

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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.

AWESOMEEE  May 11, 2015

#1
+81090
+15

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 }

CPhill  May 11, 2015
Sort:

#1
+81090
+15

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 }

CPhill  May 11, 2015
#2
+91510
+10

I always like these questions

Thanks CPhill and Awesomeee

Melody  May 12, 2015

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