there are 3 children in a family. the oldest is twice as old as the youngest. the sum of the ages of the younger two is three more than the age of the oldest. the sum of their ages is 19. how old is each child?
2006-06-23 13:41:27 · 10 answers · asked by cute_penguin21 1 in Science & Mathematics ➔ Mathematics
pretty pl include how to do it
2006-06-23 14:00:06 · update #1
x = youngest
2x = oldest
y = middle
x + y = 2x + 3
x + y + 2x = 19
Use these two simultaneous equations to solve for each variable.
x + y = 2x + 3
y = x + 3; use this to substitute into the other equation
x + (x + 3) + 2x = 19
4x + 3 = 19
4x = 16
x = 4; substitute into above statement
y = x + 3
y = 4 + 3 = 7
So the ages of the children are 4, 7, and 8
2006-06-23 15:59:37 · answer #1 · answered by jimbob 6 · 0⤊ 0⤋
x= the age of the oldest (I didn't use the letter o cause it's like zero
y= the age of the youngest
m= the age of the middle kid
x=2y (the oldest is twice the age of the youngest)
y+m=x+3 (the sum of th ages of the younger two is three more than the age of the oldest)
y+m+x= 19
There are the equations, and there are several ways to solve them of course. I would substitute then combine, but you or your teacher may prefer a more systematic approach.
substiting the first equation into the second and third we get these two
y+m=2y+3 and a little algebra gives m-y=3
y+m+2y = 19 which becomes m+3y=19
subtract the top one from the bottom and get 4y=16 or y=4
tadaaa!
substituting back in the x=2y we see that x=8
and finally substituting in the handy m+3y = 19 above we get
m + 12 = 19 or m=7
wasn't that fun
you can do this
think it through, work it out, practice
math skills are worth working for
2006-06-23 21:03:13 · answer #2 · answered by enginerd 6 · 0⤊ 0⤋
rewrite the question in math symbols.
x = youngest age
y = middle age
z = oldest age
the oldest is twice as old as the youngest: z = 2x
the sum of the two younger is three more than the oldest:
x + y = 3 + z
the sum of their ages is 19: x + y + z = 19
You have:
z = 2x
x + y = 3 + z
x + y + z =19
Now solve by replacing variables. Meaning, since z = 2x, rewrite x + y + z = 19 using 2x instead of z
z = 2x
x + y + 2x = 19
x + y = 3 + 2x
Simplify the equations:
y + 3x = 19
y - x = 3 or y = x + 3
Replace x + 3 for y in y + 3x = 19:
x + 3 + 3x = 19
4x + 3 = 19
4x = 16
x = 4
Youngest child is 4 years old
Since z = 2x, oldest child is 8 years old
Since x + y + z = 19, and 4 + y + 8 = 19
y = 7, Middle child is 7 years old
2006-06-23 22:56:52 · answer #3 · answered by Anonymous · 0⤊ 0⤋
6
2006-06-23 20:47:07 · answer #4 · answered by baby 2 · 0⤊ 0⤋
Oldest = 8
Middle = 7
youngest = 4
2006-06-23 20:49:52 · answer #5 · answered by Tony V 2 · 0⤊ 0⤋
Don't apologize for asking questions -- asking questions is GOOD. What would be bad would be not using the answers to try to learn something -- for example, just copying other people's solutions onto your homework assignment and not even thinking about the problem at all. (I hope there aren't too many people who do that.)
Add a little more to your future questions showing what progress you've made on your own and where you're stuck. That will help people help you learn. Good luck, and keep the questions coming ...
2006-06-23 20:54:58 · answer #6 · answered by Steve H 5 · 0⤊ 0⤋
youngest:4
middle:7
oldest:8
proses of elimanation and
8+4=12
12-19=7
2006-06-23 22:04:33 · answer #7 · answered by monkyodoom 2 · 0⤊ 0⤋
4, 7, 8 is correct.
Please do ask more questions.
2006-06-23 20:57:57 · answer #8 · answered by ? 6 · 0⤊ 0⤋
4,7, and 8
2006-06-23 20:47:08 · answer #9 · answered by Abby 2 · 0⤊ 0⤋
your moms cottage cheese butt.....
2006-06-23 20:44:32 · answer #10 · answered by A Dizzle 4 · 0⤊ 0⤋