Answer:
The possible values of your age are 16, 17, 18, 19, 20, 21, 22, 23, and 24.
Explanation:
Let a be current age.
The first equation tells us that:
4/5a > 3/4(a+1).
First, we expand the parenthesis by multiplying 3/4 by a+1.
4/5a > 3/4a +3/4.
Now we move all like terms to their own side of the inequality. All terms with a variable like 'a' will go to the left and all therms without a variable will go to the right.
4/5a -3/4a > 3/4.
We can now find a common denominator. LCM(5,4) = 20.
16/20a - 15/20a > 15/20.
We can now subtract terms with a variable.
1/20a > 15/20.
We can multiply each fraction by 20 to get rid of the denominators.
20a > 300
Now, we divide by 20 to get a alone.
a > 15
The current age has to be greater than 15.
The second equation tells us that:
4/5a > 5/6(a-1).
To solve, we isolate a. First, we expand the parenthesis by multiplying 5/6 by a-1.
4/5a > 5/6a - 5/6.
Next, we move all like terms to one side of the inequality. We'll move all the terms with 'a' in it to the left side and all the terms without 'a' to the right side.
4/5a - 5/6a > -5/6.
We can find a common denominator between all the fractions. The least common multiple of 5 and 6 is 30.
24/30a - 25/30a > -25/30.
Now, we can subtract like terms.
-1/30a > -25/30.
We multiply both sides by 30 to get rid of the denominators.
-30a > -750.
We divided both side by -30. We make sure to switch the direction of the sign because we divided by a negative number.
a < 25.
The current age has to be less than 25.
We know that a > 15 and a < 25. A better way of writing this would be:
15 < a < 25. This tells us a has to be greater than 15 but less than 25. The integers between 15 and 25 are 16, 17, 18, 19, 20, 21, 22, 23, and 24.