Age Problem.. ^_^

Sum of ages now=48

In 8 years, sum of ages will be =48+16=64

as Ted will be 3 times as old as Dave.that means their age's ratio will be =3:1

now, $\frac{64}{4}$ = $16$

so, Teds age will be = $16 \times 3$ = $48$ and Daves age will be = $16 \times 1$ = $16$ years old

so, current age of Ted is = $48-8$ = $40$ years old and current age of Dave is= $16-8$ = $8$ years old

Sum of ages now=48 In 8 years, sum of ages=48+16=64 Ages such that Dave is three times the age of Ted. Ted=16, Dave=48. But this is our answer for 8 years in the future so Ted current age=8, Dave current age=40

$D=present~age~of~Dave$

$T=present~age~of~Ted$

At present: $D+T=48$ $\implies$ $T=48-D$ $\color{#D61F06}(1)$

Eight years from now: $T+8=3(D+8)$ $\color{#D61F06}(2)$

Substitute $\color{#D61F06}(1)$ in $\color{#D61F06}(2)$ ,

$48-D+8=3D+24$ $\implies$ $56=4D+24$ $\implies$ $4D=56-24$ $\implies$ $\color{#3D99F6}\boxed{D=8}$

It follows that,

$T=48-8$ $\implies$ $\color{#3D99F6}\boxed{T=40}$

D=Dave's age, T=Ted's age

D+T=48, and T+8=3(D+8), which then becomes T+8=3D+24 If we solve the 2nd equation for T, we get T=3D+24-8, or T=3D+16

If we use this value to substitute T in the 1st equation, we get: D+(3D+16)=48 4D+16=48 4D=48-16 4D=32 D=32/4 D=8

This means that Dave is 8, so now we can solve for T, using: D+T=48 8+T=48 T=48-8 T=40

So Ted is 40, and Dave is 8.

Have $t = Ted$ and $d = Dave$

From the information given we can obtain two equations

1. $t+d = 48$

2. $t+8 = 3(d+8)$

Re-arranging both equations to get two equations for $t$ gives us

1. $t+d = 48 \Rightarrow t = 48 - d$

2. $t + 8 = 3(d + 8) \Rightarrow t = 3(d + 8) - 8 \Rightarrow t = 3d + 16$

Using simultaneous equations gives us

$48 - d = 3d + 16$

Simplifying this gives us a value for $d$

$48 - d = 3d + 16 \Rightarrow 32 - d = 3d \Rightarrow 32 = 4d \Rightarrow d = 8$

Now that we have a value for $d$ we can now work out a value for $t$

$t = 48 - d \Rightarrow t = 48 - (8) = 40$

So $t = 40$ and $d = 8$

Let: x = age of ted 48-x = age of dave

Therefore,

x+8 = 3(48-x+8) x+8 = 3(56-x) x+8 = 168-3x 4x = 160 x = 40

Then,

Age of ted is 40 years old and 8 years old is the age of dave...