# Thread: Fraction Question - Urgent

1. ## Fraction Question - Urgent

Linda is 9/10 as tall as patrick and 3/4 as tall as Ali. If the total height of the 3 pupils is 418.5 cm, how much taller is Ali than Patrick? Please help me and tell me how you get the answer step by step. Thanks

2. Originally Posted by aznmartinjai
Linda is 9/10 as tall as patrick and 3/4 as tall as Ali. If the total height of the 3 pupils is 418.5 cm, how much taller is Ali than Patrick? Please help me and tell me how you get the answer step by step. Thanks
We have three people, with three unknown heights. Call the respective heights of Linda, Patrick, and Ali $\displaystyle h_1,\,h_2,\text{ and }h_3$.

Since Linda's height is $\displaystyle \frac9{10}$ that of Patrick, we have

$\displaystyle h_1 = \frac9{10}\cdot h_2.$

Similarly, for Linda and Ali we have

$\displaystyle h_1 = \frac34\cdot h_3.$

But we further know that the sum of all three heights is 418.5 cm. This gives:

$\displaystyle h_1 + h_2 + h_3 = 418.5\text{ cm}.$

You now have three equations with three unknowns. Can you solve this system?

3. Let $\displaystyle L$ = Linda, $\displaystyle P$= Patrick, $\displaystyle A$= ali.
$\displaystyle L=\frac{9}{10}P, L = \frac{3}{4}A$
we have
$\displaystyle P=\frac{10}{9}L, A=\frac{4}{3}L$
$\displaystyle P+A+L=418.5$
now just replace the $\displaystyle P$ and $\displaystyle A$ as expressed with $\displaystyle L$above and you'll find the height of Lisa first, then others.

4. i still don't know how to get h2? can you tell me please?

5. Originally Posted by aznmartinjai
i still don't know how to get h2? can you tell me please?
If you were able to find $\displaystyle h_1$ and $\displaystyle h_3$, then you can simply substitute them into the third equation and solve for $\displaystyle h_2$.

6. so h1 h3 are the same number?

7. Originally Posted by aznmartinjai
so h1 h3 are the same number?
No, they should be distinct. What values did you get? Show some of your work.

8. i dont know how you get h1....

9. h1 = 9/10 x 50 = 45 and h2 = 3/4 x 60 = 45 until now you say thier distince. I wonder if you can tell me so i can study it and better understand the problem..

10. Originally Posted by aznmartinjai
i dont know how you get h1....
Substitute equation (2) into equation (1) to get h1 in terms of h3.
Substitute this expression for h1 and the expression for h2 into equation (3) and solve for h3.
Use the value of h3 to get the value of h2.
Use the value of h2 to get the value of h1.

11. Originally Posted by aznmartinjai
h1 = 9/10 x 50 = 45 and h2 = 3/4 x 60 = 45 until now you say thier distince.
Hold on, I just realize that I misread the problem. I thought it said Patrick (not Linda) was $\displaystyle \frac34$ as tall as Ali. Let me correct my post.

Edit: Alright, the values should still be distinct. Where did you get the 50 and the 60 in your two equations above?

12. is this right?

L = 121.5 cm
P = 135 cm
A = 162 cm

A - P = 27 cm

13. Originally Posted by aznmartinjai
is this right?

L = 121.5 cm
P = 135 cm
A = 162 cm

A - P = 27 cm
Correct!

14. ty recknor and also what was your step by step to the answer? i also want to see how you did it

15. Originally Posted by aznmartinjai
ty recknor and also what was your step by step to the answer? i also want to see how you did it
From the three equations in my first post (now corrected), I just used simple substitution to solve the system: I solved the first two equations for $\displaystyle h_2$ and $\displaystyle h_3,$ respectively, and then substituted into the third equation, which could then be solved for $\displaystyle h_1$.

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