The present ages of a husband and wife are in the ratio of seven to six. Five years ago the ratio was six to five. What are their ages now?
The choices are:
h: 35 yrs and w: 30 yrs
h: 41 yrs and w: 35 yrs
h: 49 yrs and w: 42 yrs
h: 56 yrs and w: 49 yrs
2006-10-11 09:43:40 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Their ages are 35 and 30.
2006-10-11 09:50:13 · answer #1 · answered by sexy_as_well 2 · 0⤊ 0⤋
The first and third ones are ratio 7:6, so it's either 35 and 30 or 49 and 42. Subtract 5 from those and get 30:25 and 44:37, and the ratio is 6:5 with 30:25, so it's the first one, 35 and 30.
2006-10-11 16:51:25 · answer #2 · answered by Tim J 4 · 1⤊ 0⤋
Let x = present age of husband
Let y = current age of wife
Currently 6x = 7y
5 years ago:
5(x-5) = 6(y-5)
or 5x - 25 = 6y - 30
Now we have a system of two equations and we can solve for x.
Multiply (6x = 7y) by 6 to get
36x = 42 y
Multiply (5x - 25 = 6y - 30) by 7 to get
35x - 175 = 42y - 210
Substitute 36x for 42y
35x - 175 = 36x - 210
Add 210 to both sides and subtract 35 x from both sides
35x - 35x - 175 + 210 = 36x - 35x - 210 + 210
Simplify
35 = x
To get the wife's age, go back to 6x = 7y and substitute 35 for x
6(35) = 7y
210 = 7y
30 = y
The husband is currently 35 years old.and his wife is currently 30 years old.
You can double check that this is in a 7:6 ratio.
As a further check, five years ago he was 30 and she was 25 which was in a 6:5 ratio.
2006-10-11 16:53:53 · answer #3 · answered by Draco Moonbeam 3 · 0⤊ 0⤋
The answer is the husband is 35 and the wife is 30.
(7) (6)
5 years ago the husband was 30 and the wife was 25.
(6) (5)
2006-10-11 17:04:06 · answer #4 · answered by Inferno13 6 · 0⤊ 0⤋
Currently, h/w = 7/6.
From 5 years ago, (h-5)/(w-5) = 6/5.
Cross-multiply both: 6h=7w, and
5(h-5) = 6(w-5). Expand this, and get 5h-25=6w-30, or 5h=6w-5.
Now you have 6h=7w, and 5h=6w-5.
Subtract these two equations, and you get h=w+5. So their ages are 5 apart.
The only choice for which this is the case is the first one.
2006-10-11 16:53:13 · answer #5 · answered by James L 5 · 0⤊ 0⤋
35-30 trust me
2006-10-11 16:53:18 · answer #6 · answered by this_kid_is_hot_15_09 2 · 0⤊ 0⤋