im having a lot of difficulty with homework?

Question

the present ages of a husband and wife are in ration 7 to 6 and five years ago was 6 to 5 find theirt ages now
the difference of two numbers if 72 if the larger number is divided by the smaller one the quotient is 7 and the remainder is 6 find the numbers.
the numerator and the denominator of a fraction are 13 to 50 respectively.when a certain # is added to this numerator and subtracted from the denominator the resultin fraction has a numerator to denominator ratio 1 to 2 find the number

an automobiles radiator has a capacity of 15 quarts and is currently 12 quarts of a 30 % anti freeze solution.
a)how many quarts of antifreze must be added to strenghten the solution to 40%
b)if the radiator is filled to capacity with antifrez what will be the strength of the solution?

Answer 1

Age question
H = husbands age
W = wife's age
H/W = 7/6
ie 6H = 7W

5 years ago
(H-5) / (W-5) = 6/5
5H - 25 = 6W - 30
5H = 6W - 5
6H = 7.2W - 6
7W = 7.2W - 6 because 6H = 7W
0.2W = 6
W = 30
H = 35

The other questions are very similar. Just follow the wording and try to fo rmulate simultaneous equations.

Answer 2

Not going to do your homework for you. But here is how you set the problems up. Hope they help you learn this material.



y/x = 7/6
(y-5)/(x-5) = 6/5



x - y = 72
x = 7y + 6



(13 + x)/(50 - x) = 1/2

a)how many quarts of antifreze must be added to strenghten the solution to 40%>

12(30) + x(100) = (12 + x)(40)



12(30) + (15 - 12)(100) = 15(x)

Answer 3

1) ago: H:W
6:5
x:y
then by cross multiplication we get 5x=6y.
Now H:W
7:6
x+5:y+5
then by cross multiplication we get 6(x+5)=7(y+5)
then 6x+30=7y+35 "-30"
6x=7y+5
we have 2 equations 5x=6y "multiply by 6"
6x=7y+5 "multiply by 5"
then 30X=36Y
30X=35Y+25 (subtract)

0=Y-25 then y=25 "age of wife before 5 years"
5X=6(25) then x=30 "age of husband before 5 years"

2) we have 2 equations :
X-Y=72 ------->(1) X/Y = 7 6/Y ----> (2)

2. then X/Y = (7Y+6)/Y (*Y)
then x=7y+6
solve the 2 equations x=7y+6 and x-y=72 as in ex.1
the answer is:83,11

3) (13+X)/(50-x) = 1/2 cross multiply
50-x=26+2x -50
-x=2x-24 *-1
x=24-2x +2x
3x=24 /3
x=8
this #=8

4)a. ??: 40%
12 quarts:30%
therefore ?? = 40*12/30
=16
we have already 12 quarts so we need 16-12=4 quarts more.

b) 15 quarts:??
12 quarts : 30%
therfore ?? = 30*15/12
=37.5%

Answer 4

Let the present ages of the husband and wife be 7x and 6x.Hence 5 years ago their ages were 7x-5 and 6x-5 respectively.
By the problem
7x-5/6x-5=6/5
=>36x-30=35x-25 [by cross multiplication]
=>36x-35x=-25+30
x=5
The present age of the husband is7*5 ot 35 years and that of wife is 6*5 or 30 years
2.Let the smaller no. be x.hence the larger one is x+72
According to the problem,
(x+72)/x=7+6/x
=>x+72/x=(7x+6)/x
=>x+72=7x+6 [eliminating common denominator x from both sides]
=>x-7x=6-72
=> -6x= -66
x=11
Therefore,the smaller number is 11 and the larger no. is 11+72=83
3.let the number added and subtracted be n
Therefore,by the problem,
(13+x)/(50-x)=1/2
=> 26+2x=50-x [by cross multiplication]
=> 2x+x=50-26
=>3x=24
x=8
Therefore,the no. is 8

Answer 5

If you have 12 quarts of 30% solution, then 30% * 12 = 3.6 quarts of antifreeze and 8.4 quarts of water.

We are going to add pure antifreeze in the amount of x quarts to bring the ration up to 40%

(3.6 + x) / (12 + x) = 40% = .4

(3.6 + x) = (12 + x) * .4
3.6 + x = 4.8 + .4x

I'm going to multiply both sides by 10 to get rid of decimals.

36 + 10x = 48 + 4x
6x = 12
x = 2

If I add 2 quarts of antifreeze, I will have 5.6 quarts of antifreeze / 14 quarts total = 40%



On the other hand, if I add 3 quarts of water to make a total of 15 quarts, I will get
3.6 quarts antifreeze / 15 quarts total = .24 = 24% solution

Answer 6

1. 35,30
2. 11,66... use the equation x - y = 72, x - 6 = 7y
3. (13 + x)/(50 - x) = 1/2, x=8