The ratio of their ages is 5:7 (that is, x/y = 5/7). In three years time the ratio of their ages will be 3:4. Find their present ages.
2007-02-24 12:02:48 · 12 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
x/y = 5/7
x = 5y/7
(x+3) / (y+3) = 3/4
4x + 12 = 3y + 9
20y/7 + 12 = 3y + 9
20y + 84 = 21y + 63
21y - 20y = 84 - 63
y = 21
x = 5*21 / 7
x = 15
2007-02-24 12:10:32 · answer #1 · answered by M. Abuhelwa 5 · 0⤊ 1⤋
Their ages now are 18 and 24.
To make it easy, will solve the problem with the variables being their present ages, a and b
so, three years ago their age was
(a-3)/(b-3)=5/7
and now
a/b=3/4
solving the system we get the above values for the present ages and 18/24= 3/4
and 3 years ago
15/21=5/7
2007-02-24 20:24:07 · answer #2 · answered by Good Advice 2 · 0⤊ 1⤋
[18 and 24 years old] is the Answer
how I work it out
your second ratio is 3:4 so i add them together
3+4=7
7X6=42
3(first number from second ratio of your question)X6=18
4(seond from second ratio of your question)X6=24
18/6=3
24/6=4
[this is your second equation 3:4]
18-3=15
15/3=5*
24-3=21
21/3=7*
this is your first equation5:7
(this just bring it back to first ratio which is the answer)
DAVE=15
JILL=21
2007-02-24 20:35:03 · answer #3 · answered by ellalee1730917309 1 · 0⤊ 0⤋
x/y = 5/7
(x + 3)/(y + 3) = 3/4
4(x + 3) = 3(y + 3)
4x + 12 = 3y + 9
4x + 3 = 3y
y = (4/3)x + 1
x/((4/3)x + 1) = (5/7)
x/((4x + 3)/3) = 5/7
(3x)/(4x + 3) = 5/7
7(3x) = 5(4x + 3)
21x = 20x + 15
x = 15
y = (4/3)(15) + 1
y = (60/3) + 1
y = 20 + 1
y = 21
Dave is 15 years old
Jill is 21 years old
2007-02-24 20:26:16 · answer #4 · answered by Sherman81 6 · 0⤊ 0⤋
x/y = 5/7
multiply both sides by y:
x = 5y / 7
in three years,
(x + 3) / (y + 3) = 3/4
cross multiply
4x + 12 = 3y + 9
substitute x = 5y / 7 and solve for y
4 (5y / 7) + 12 = 3y + 9
(20/7) y + 12 = 3y + 9
(-1/7)y = -3
y = 21
x = 5y / 7
x = 5(21) / 7
x = 15
2007-02-24 20:10:00 · answer #5 · answered by Anonymous · 0⤊ 1⤋
(5x + 3)/ (7x+3) = 3/4
21x+9 = 20x+12
x = 3
in 3 years, the ages are 18 and 25
that means now, the ages are 15 and 21
2007-02-24 20:10:18 · answer #6 · answered by 7 · 0⤊ 1⤋
x/y = 5/7
7x = 5y
21x = 15y (i)
(x + 3)/(y + 3) = 3/4
4(x + 3) = 3(y + 3)
4x + 12 = 3y + 9
4x + 3 = 3y
20x + 15 = 15y (ii)
Substitute (i) into (ii)
20x + 15 = 21x
x = 15
7x = 5y
105 = 5y
y = 21
Dave is 15, Jill is 21
2007-02-24 20:07:50 · answer #7 · answered by Tom :: Athier than Thou 6 · 0⤊ 1⤋
17 and 23 years.
2007-02-24 20:04:54 · answer #8 · answered by lulu 6 · 0⤊ 3⤋
cross multiply stop trying to get your homework done on here
2007-02-24 20:05:16 · answer #9 · answered by jumanjisapikey 3 · 0⤊ 1⤋
x/y=5/7
x+3/y+3=3/4
so easy !!! system of equation
2007-02-24 20:05:15 · answer #10 · answered by Anonymous · 0⤊ 3⤋