SOLUTION: If a:b =c:d =5:7, find (a+c):(b+d).

Question 1013841: If a:b =c:d =5:7, find (a+c):(b+d).
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

If , find

=>

=
=
=
=
=
=

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your solution is (a+c)/(b+d) = 5/7.

you can find it easily by just assuming some values for a and b and c and d and solving.

you can also find it in terms of a and b and c and d much more arduously by performing algebra on the variables directly.

in that case you will get (a+c)/(b+d) = (25*(b+d))/(49*(a+c)).

when you replace a and b and c and d with qualifying numbers, the ratio will wind up being the same, i.e. it will be 5/7.

first i'll do it using numbers.

then i'll do it using variables.

your ratio is a:b = c:d = 5:7.

this can also be written as a/b = c/d = 5/7

this means that a/b = 5/7 and that c/d = 5/7.

if we assume that a is 5 and b is 7, then the ratio is 5/7 for them.

if we assume that c is 5 and d is 7, then the ratio is 5/7 for them.

since a = 5 and b = 7 and c = 5 and d = 7, then the ratio of (a+c)/(b+d) becomes (5+5)/(7+7) which becomes 10/14 which simplifies to 5/7.

you can assume that c = 10 and d = 14, or c = 15 and d = 21.
as long as the ratio of c/d simplifies to 5/7, all those values are good and will lead to the same conclusion.

for example:

assume a = 5 and b = 7 and c = 15 and d = 21.

(a+c) = 20
(b + d) = 28

(a+c)/(b+d) = 20/28 which simplifies to 5/7.

with letters it becomes a little more complex, but you'll get an answer that will be equivalent to the answer that you got with numbers.

start with a/b = 5/7 and c/d = 5/7

cross multiply to get 7a = 5b and 7c = 5d

solve for a to get a = 5b/7
solve for b to get b = 7a/5
solve for c to get c = 5d/7
solve for d to get d = 7c/5

a+c is equal to 5b/7 + 5d/7 = (5b+5d)/7 = 5(b+d)/7.

b+d is equal to 7a/5 + 7c/5 = (7a+7c)/5 = 7(a+c)/5.

(a+c)/(b+d) = 5(b+d)/7 divided by 7(a+c)/5.

this is equivalent to 5(b+d)/7 times 5/(7(a+c))

this is equivalent to 5(b+d)*5/ (7*7(a+c))

simplify further to get

to confirm, we replace a,b,c,d with qualifying values.

we'll assume a = 5, b = 7, c = 15, d = 21

the equation of becomes

simplify this to get

perform the multiplication to get

when you simplify this, you will find that it is equal to 5/7.

RELATED QUESTIONS
a + b + c + d = 7 2a - b + c - 2d= -13 3a + b - 2c - d = 5 4a - b + 3c - d = -10 (answered by math_helper)
if (a)/(b)<(c)/(d) , show that (a)/(b)<(a+c)/(b+d)<(c)/(d) (answered by richard1234)
A/B=(C+D)/D (answered by Alan3354)
if b/d=a/b will... (answered by rapaljer)
If a=2,b=3,c=4,d=5:solve... (answered by ValorousDawn)
A/b=c/d... (answered by checkley77,stanbon)
If a>b+c and d> b+a then: A. a>d B. b>a+d C. c>a-b D. d>c (answered by Theo)
A={2,4,6,8,10} B={1,3,5,7,9,} C={1,2,3,4,5,6} D={3,4,6,9,} evaluate it : 1.A... (answered by Edwin McCravy)
a= bx3, b=d-10, c=the sum of 7 and 3, d=c+c, a= b= c=... (answered by Fombitz)