at the moment john is 5 years older than mary. in 7 years time marys age will be three quarters of johns age. how old are they at the present?
2006-06-23 13:17:56 · 7 answers · asked by cute_penguin21 1 in Science & Mathematics ➔ Mathematics
John is 13
Mary is 8
2006-06-23 13:23:40 · answer #1 · answered by c_wag03 4 · 0⤊ 0⤋
Mary is 8, John is 13
2006-06-23 13:25:31 · answer #2 · answered by Tony V 2 · 0⤊ 0⤋
Looks like a homework problem, but perhaps a little help with this one will send you winging away doing your homework and learning math with great leaps and bounds.
let m = mary's age now
let j = johns age now (their ages now is what we are trying to find)
the first sentance tells us that johns age now (j) is 5 more than mary's age now (m) so..
j=m+5 there's one equation
the second sentence tells us that in 7 more years (when both john and mary's age will be 7 more than it is now) that mary's age then (m+7) will be three quarters of johns age then (j+7)
so
(m+7) = 3/4 * (j+7)
a little algegra yields 4m+28 =3j+21 and 3j=4m+28-21
or 3j=4m+7
the two equations
3j=4m+7
j=m+5
there are several ways to solve this set but I like to
multiply the bottom equation by 3 giving 3j=3m+15
3j=4m+7
3j=3m+15
subtract the bottom equation from top yielding
0=m-8 or m=8 (thats mary's age now)
and then substituing in first equation j=m+5 we get j=8+5 or
j=13 (johns age now) remember mary is 8 now
that was fun, lets check it:
now, john is 5 years older than mary john 13, mary 8 check
in 7 years, john will be 20, mary 15, and mary will be 3/4 of john's age check again
excellent
good luck on the rest of your homework
2006-06-23 13:33:59 · answer #3 · answered by enginerd 6 · 0⤊ 0⤋
let:
Mary's age= x
john's age=x + 5 since john is now 5 years older than mary
after seven years (x+7),
mary's age will be three fourths of john's age after 7years .75(x+5+7)
x + 7 = .75(x + 5 + 7)
now you just work it out for x, after you get what x is, that will be mary's age and x+5 will be john's age. when you work it out, remember there is
an invisible 1 in front of each variable that doesnt have any number in front of it. like when it's x , it's same thing as 1x.
2006-06-23 13:44:04 · answer #4 · answered by mr.smartguy 1 · 0⤊ 0⤋
j = m + 5
m + 7 = 3(j + 7)/4
4m + 28 = 3(j + 7)
4m + 28 = 3(m + 5 + 7)
4m + 28 = 3(m + 12
4m + 28 = 3m + 36
m + 28 = 36
m = 8
j = m + 5
j = 13
2006-06-23 13:37:32 · answer #5 · answered by jmdanial 4 · 0⤊ 0⤋
j = m + 5
m + 7 = 3(j + 7)/4
4m + 28 = 3(j + 7)
4m + 28 = 3(m + 5 + 7)
4m + 28 = 3(m + 12
4m + 28 = 3m + 36
m + 28 = 36
m = 8
j = m + 5
j = 13
2006-06-23 13:23:45 · answer #6 · answered by Guelph 5 · 0⤊ 0⤋
John is 13
Mary is 8
2006-06-23 15:07:42 · answer #7 · answered by josh 1 · 0⤊ 0⤋