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?
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.
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?
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 $\displaystyle h_1$.