Please help with my son's homework question.?

Question

Ryan is a quarter of Susan's age at present.
In four years time, he will be one third of her age.
However, four years ago, Ryan was one-seventh of Susan's age.
How old are they now?

Please show workings if you can.

Regards
A hopeless mum (ooh and son)

Hey Guys don't slate me i'm just trying to understand so I can help him understand. If you dont get that then heyho.

Answer 1

You've already got the solution and answer but I would like to say well done for taking the trouble to help your son. Homework is not set just for children to struggle with but to encourage parents/families to understand what the child is expected to be able to do and find the time to support. By all means tell the teacher that he has had help, but I can assure you that they will be pleased that you took time and trouble to try and help him.

(I would certainly NOT class you as a hopeless mum or son - he's a lucky boy!)

Answer 2

R = Ryan's age now
S = Susan's age now

R = 1/4 * S because Ryan is 1/4 of Susan's age

(R+4) = 1/3 * (S+4) because in 4 years, Ryan will be 1/3 of Susan's age

(R-4) = 1/7* (S-4) because 4 years ago, Ryan was 1/7 of Susan's age

Use any two of those equations to solve for a variable.

If you add the bottom two together and multiply all terms by 21 (which is 3*7... comes from the 1/3 and 1/7 in the clues) you get...

42R = 10S + 16

Since R=1/4 S, substitute for either variable...

42 * 1/4 S = 10S + 16

S = 32

R = 1/4 (S) = 1/4 (32) = 8

Susan is 32 and Ryan is 8. It works out if you plug in these ages into the clues.

Answer 3

Ryan = 8 Susan = 32
12x3 = 36 = 32+4
4x7=28 = 32-4

Answer 4

r = Ryan's age now
s = Susan's age now

Now convert the words to equations:

Ryan is a quarter of Susan's age:
1) r = s/4

In four years time, he will be 1/3 of her age (at that time).
2) (r+4) = (s+4)/3

Four years ago, Ryan was 1/7 of her age (at that time).
3) (r-4) = (s-4)/7

You only need a couple of these equations. Start by using equation 1. r = s/4 can be rewritten as s = 4r. Now substitute 4r in place of s in equation 2.

(r + 4) = (4r + 4)/3

Multiply by 3:
3r + 12 = 4r + 4

Subtract 4 from both sides:
3r + 12 - 4 = 4r
3r + 8 = 4r

Subtract 3r from both sides:
8 = 4r - 3r
8 = r
r = 8

Now solve for s (using equation 1 again):
s = 4r
s = 32

Double check your work:
Ages now are Ryan (8) and Susan (32) = 1/4
Four years from now they will be Ryan (12) and Susan (36) = 1/3
Four years ago they were Ryan (4) and Susan (28) = 1/7.

So the answer is:
Ryan is 8 years old and Susan is 32 years old.

Answer 5

Take Ryan's age as R and Susan's as S

R= 1/4 S and
R+4 = 1/3 (s+4) :in 4 years time.

Mulitply everthin by 12 to get rid of the fractions,

12R = 3S and
12R+48 = 4(S+16)
=> 12R+48 = 4S+16

since 12R = 3S
=> 3S+48 = 4S+16

=> 3S+32 = 4S

minus 3S from each side and you get

32 = S

Therefore Susan is 32, put this back into equation 1 and Ryan is 8, then you can just use the last bit (4 years ago) to check.

Hope this helps, its years since I have done simultaneous equations, am amazed its still in my head somewhere!

Answer 6

Ryan is 8 at present. Susan is 32.
In four years time, Susan will be 36, and Ryan will be 12 (1/3).
Four years ago, Susan was 28, and Ryan was 4. (1/7)

Sorry...I don't have a formula. I just guessed a few numbers that were divisible evenly by 4. I love math!

The people who are putting you down for asking for help....have obviously never tried to help their child do homework.

Answer 7

ryan is 8 sue 32 now ,8and 32 is a quarter add 4 years 12 and 36 what is 1 third ,take 4 years off the present age 4 and 28 what is 1 seventh so the age now is 8 and 32 hope this looks right to you.

Answer 8

Ryan is 8 and Susan is 32 8x4=32

Add 4

Making
Ryan 12 and Susan 36 12x3=36

Take 4 away
Making
Ryan 4 and Susan 28 4x7=28

Top answer is the final answer

Answer 9

Here's how it works:
Let x be Ryan's age. Let y be Susan's age.

Ryan is 1/4 Susan's age now.
x = y/4

In four years, he will be 1/3 her age.
(x+4) = (y+4)/3
3x + 12 = y + 4
3x = y - 8
x = (y - 8) / 3

But you already know that x = y/4, from above. So
y/4 = (y - 8)/3
12 (y/4) = 12 * (y - 8)/3
3y = 4y - 32
y = 32

Since x = y/4, x = 8. You don't even need the third part of the question.

Answer 10

Ryan is 8 and Susan is 32.

Had to get my brain in gear for that one, years since I did Maths. Can't really remember how to write the equation for it. Just worked with a few different numbers.