Question

The amount of lemon syrup to the amount of water in Cup A is in the ratio 2 : 5. The amount of lemon syrup to the amount of water in Cup B is in the ratio 1 : 6. There is an equal amount of lemon syrup in both cups. Cup B contains 189 mℓ more water than Cup A. What is the amount of lemon syrup in Cup A? Leave the answer in mℓ

Answer 1

cupA
lemon : water = 2x : 5x
cupB
lemon : water = y : 6y

There is an equal amount of lemon syrup in both cups
---> y = 2x
Cup B contains 189 mℓ more water than Cup A
---> 6y = 5x + 189
use substitution, ...
6(2x) = 5x + 189
7x = 189
x = 27 , then y = 54
now we can find the amount of each in both cups ...

lemon in cupA = 2x = 54 ml

Answer 2

Cup B = Cb
Cup A = Ca
Lemon syrup = L
L/Ca = 2/5 — (1)
L = 2 Ca/5 —— *
L/Cb = 1/6
L = Cb/6 — (2)
Cb = Ca + 189 - (3)
Where L in Ca = L in Cb
2 Ca/5 = Cb/6
Cb = (2 * Ca * 6)/5
Cb = 12 Ca/5
Substitute Cb in (3)
12/5 Ca = Ca + 189 {Convert like term}
12/5 Ca - Ca = 189

(12 Ca - 5 Ca)/5 = 189
7 Ca = 5 * 189
Ca = (5 * 189)/7
Ca = 27 * 5
Ca = 135 ml
Substitute Ca into (*)
L = (2 * 135 ml)/5
L = 27 ml * 2
L = 54 ml is present in Cup A