Jade's age now is the same as Timmy's five years hence. Timmy's age six years ago was half Jade's age now. Find the present age of each.
let:
J=jades age now
T=Timmy's age now
interpretation:
J=T+5-----eqtn.1
T-6=J/2----eqtn.2
substitute eqtn 1 to 2
T-6=(T+5)/2
2(T-6)=T+5
2T-12=T+5
T=17
Timmy's age now is 17 yrs. old
Subs. to eqtn. 2
J=T+5
J=17+5
J=22
Jade's age now is 22 yrs. old.
check:
Timmy age 6 years ago is half of jades
T-6=J/2
17-6=22/2
11=11
check!!!!!!!!!!!!!!!!!
To solve this problem, we can set up equations based on the given information.
Let's assume Jade's current age is J years, and Timmy's current age is T years.
From the first statement, we know that Jade's age now (J) is the same as Timmy's age five years from now (T + 5). So, we can write the equation:
J = T + 5
From the second statement, we know that Timmy's age six years ago (T - 6) was half of Jade's current age (J). So, we can write the equation:
T - 6 = (1/2) * J
Now we have a system of two equations with two variables. We can solve this system by substituting the value of J from the first equation into the second equation:
T - 6 = (1/2) * (T + 5)
Multiplying both sides of the equation by 2 to eliminate the fraction:
2(T - 6) = T + 5
Expanding the equation:
2T - 12 = T + 5
Simplifying the equation, we get:
2T - T = 5 + 12
T = 17
Now substitute the value of T back into the first equation to find J:
J = T + 5
J = 17 + 5
J = 22
Therefore, Timmy's present age is 17 years and Jade's present age is 22 years.