SOLUTION: Could you please help with this problem? The present ages of a husband and wife are in the ratio of seven to six, and five years ago the ratio was six to five. Find their ages n

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Question 947470: Could you please help with this problem?
The present ages of a husband and wife are in the ratio of seven to six, and five years ago the ratio was six to five. Find their ages now.
I got this formula, but I think I'm incorrect:
+%287%2Ax-5%29%2F%286%2Ax-5%29=+%286%2A%28x-5%29%29%2F%285%2A%28x-5%29%29
this gives me an answer of +65%2F36+, but I don't think it's right.
Found 3 solutions by Alan3354, MathLover1, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The present ages of a husband and wife are in the ratio of seven to six, and five years ago the ratio was six to five. Find their ages now.
I got this formula, but I think I'm incorrect:
+%287%2Ax-5%29%2F%286%2Ax-5%29=+%286%2A%28x-5%29%29%2F%285%2A%28x-5%29%29
this gives me an answer of +65%2F36+, but I don't think it's right.
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You didn't find their ages.
----
H/W = 7/6
(H-5)/(W-5) = 6/5
-----
H/W = 7/6 --> H = 7W/6
Sub for H in the 2nd eqn
(H-5)/(W-5) = 6/5
((7W/6)-5)/(W-5) = 6/5
((7W/6)-5)*5 = (W-5)*6 = 6W-30
35W/6 - 25 = 6W-30
35W - 150 = 36W - 180
W = 30
H = 35

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let the present ages of a husband be x and of a wife y
The present ages of a husband and wife are in the ratio of seven to six,
x%2Fy=7%2F6............eq.1
and five years ago the ratio was six to five.
%28x-5%29%2F%28y-5%29=6%2F5............eq.2
to find their ages now, solve this system:
x%2Fy=7%2F6............eq.1
%28x-5%29%2F%28y-5%29=6%2F5............eq.2
-------------------------------------
start with x%2Fy=7%2F6............eq.1 and solve for x

x=%287%2F6%29y ....substitute in eq.2
%28%287%2F6%29y-5%29%2F%28y-5%29=6%2F5............eq.2..solve for y

%28%287%2F6%29y-5%29%2F%28y-5%29=6%2F5 cross multiply
5%28%287%2F6%29y-5%29=6%28y-5%29
%2835%2F6%29y-25=6y-30
35y%2F6=6y-30%2B25
35y=%286y-5%296
35y=36y-30
30=36y-35y
30=y
or y=30
now find x
x=%287%2F6%29y
x=%287%2F6%2930
x=%287%2Fcross%286%291%29cross%2830%295
x=7%2A5
x=35
so, the present ages of a husband and wife are:
a husband is 35
a wife is 30
check the ratio: 35%2F30=7%2F6 =>1.166666666666667=1.166666666666667 => true
five years ago a husband was 35-5=30 and wife 30-5=25
check the ratio: 30%2F25=6%2F5 =>1.2=1.2 => true

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Could you please help with this problem?
The present ages of a husband and wife are in the ratio of seven to six, and five years ago the ratio was six to five. Find their ages now.
I got this formula, but I think I'm incorrect:
+%287%2Ax-5%29%2F%286%2Ax-5%29=+%286%2A%28x-5%29%29%2F%285%2A%28x-5%29%29
this gives me an answer of +65%2F36+, but I don't think it's right. 
Current ratio of husband's to wife's age: 7:6

Let multiplicative factor be x

Then husband’s current age is: 7x and the wife’s is: 6x

Five years ago, husband was: 7x – 5, and wife was: 6x – 5

We then get: %287x+-+5%29%2F%286x+-+5%29+=+6%2F5 ------ Ratio, 5 years ago was 6%3A5

6(6x – 5) = 5(7x – 5) -------- Cross-multiplying

36x – 30 = 35x – 25

36x – 35x = - 25 + 30

x, or multiplicative factor = 5



Husband’s current age: 7(5), or highlight_green%2835%29

Wife’s current age: 6(5), or highlight_green%2830%29