At the end of 1994, Frodo was half as old as his grandfather. The sum of the years they were born is 3838. How old will Frodo be at the end of 2007?
2007-11-01 13:12:34 · 6 answers · asked by J 3 in Science & Mathematics ➔ Mathematics
63
2007-11-01 13:20:35 · answer #1 · answered by ssssh 5 · 0⤊ 0⤋
Ok.
Let F be the year Frodo was born, let G be the year his Grandpa was born:
F + G = 3838
In 1994, Frodo was half as old as his grandfather. This means
1994 - F = ( 1994 - G) / 2
(Since 1994 - F tells us how old Frodo was in 1994 and 1994 - G tells us how old grandpa was in 1994)
So, from our first equation, we subtract G from the left side so we have:
F= 3838 - G
Now, plug this in for F into our second equation. So we have:
1994 - (3838 - G) = (1994 - G) / 2
Simplifying, we have:
-1844 + G = (1994 - G) / 2
Multiply both sides by 2:
-3688 + 2G = 1994 - G
Now add 3688 to each side
2G = 5682 - G
Now add G to both sides
3G = 5682
Now divide by 3:
G = 1894
So, Frodo's grandpa was born in 1894.
Plug this into the equation F + G = 3838. So we have:
F + 1894 = 3838
Subtract 1894 from each side
F = 1944
This means Frodo was born in 1944. So, in 2007, he will be
2007 - 1944 = 63 years old
=) Hope this helps!
2007-11-01 13:26:00 · answer #2 · answered by Ace 4 · 0⤊ 0⤋
F = Frodo's age
G = grandfather's age
2007 - F = year Frodo was born
2007 - G = year grandfather was born
2007 - F + (2007 - G) = 3838
4014 - F - G = 3838
176 - F = G
2(F-13) = G - 13 (ages in 1994)
2(F-13) = 176 - F - 13
2F - 26 = 163 - F
3F = 189
F = 63 yrs old
2007-11-01 13:24:33 · answer #3 · answered by Steve A 7 · 0⤊ 0⤋
f = Frodo's age in 1994
He was born in 1994 - f
g = Grandfather's age in 1994
He was born in 1994 - g or 1994 - 2f because
f = (1/2)g
g = 2f
(1994 - f) + (1994 - 2f) = 3838
3988 - 3f = 3838
SUBTRACT3838 from both sides and ADD 3f to both sides
3988 - 3838 = 3f
150 = 3f DIVIDE both sides by 3
50 = f
50 (2) = g
100 = g
Since Frodo was 50 in 1994 he will be 13 years older in 2007
2007 - 1994 = 13
50 + 13 = 63
2007-11-01 13:22:48 · answer #4 · answered by Anonymous · 1⤊ 0⤋
F = Frodo
G = Grandfather
F +G = 3838
1994 -F = 0.5(1994 - G )
0.5G -F = -997
F +G =3838
1.5G = 3838 -997 = 2841
G = 1894
F = 3838 -G = 3838 -1894 =1944
Frodo will be 2007 -1944 = 63 years old
2007-11-01 13:27:13 · answer #5 · answered by Anonymous · 0⤊ 0⤋
x=Frodo's age in 1994
y=grandfather's age in 1994
system of equations
y=2x
(1994-x)+(1994-y)=3838
solve for x
3988-x-y=3838
150-y=x
substitute y
150-2x=x
150=3x
x=50
solve for y
y=2(50)
y=100
find age at 2007
2007-1994=13
50+13=63
Frodo was 63 in 2007
2007-11-01 13:25:22 · answer #6 · answered by sifonblue 1 · 0⤊ 0⤋