Pippa made a litre of drink from apple juice and water in the ratio of 1 : 2. She found the taste too strong so she made a litre again in the ratio 1 : 3, but found this too weak. So she thought if she combined these two mixtures, it should be about right. What is the ratio of apple juice to water in this new mixture?
We have this
In the first mixture, we have (1/3) litre of apple juice and (2/3) litre of water
In the second mixture, we have (1/4) litre of apple juice and ( 3/4) litre of water
When we combine these we get
(1/3 + 1/4) = 7/12 litres apple juice and
(2/3 + 3/4) = 17/12 litres of water
So....the ratio is
(7/12) /(17/12) = 7 / 17 = 7 : 17 ratio of apple juice to water
We have this
In the first mixture, we have (1/3) litre of apple juice and (2/3) litre of water
In the second mixture, we have (1/4) litre of apple juice and ( 3/4) litre of water
When we combine these we get
(1/3 + 1/4) = 7/12 litres apple juice and
(2/3 + 3/4) = 17/12 litres of water
So....the ratio is
(7/12) /(17/12) = 7 / 17 = 7 : 17 ratio of apple juice to water
Pippa made a litre of drink from apple juice and water in the ratio of 1 : 2. She found the taste too strong so she made a litre again in the ratio 1 : 3, but found this too weak. So she thought if she combined these two mixtures, it should be about right. What is the ratio of apple juice to water in this new mixture?
Pippa machte einen Liter Getränk aus Apfelsaft und Wasser im Verhältnis 1: 2. Sie fand den Geschmack zu stark, so dass sie wieder einen Liter im Verhältnis 1: 3 machte, fand dies aber zu schwach. Also dachte sie, wenn sie diese beiden Mischungen kombinierte, sollte es ungefähr richtig sein. Wie ist das Verhältnis von Apfelsaft zu Wasser in dieser neuen Mischung?
\(1l=\frac{1}{3}l\ A+\frac{2}{3}l\ W\\ 1l=\frac{1}{4}l\ A+\frac{3}{4}l\ W\\ 2l=(\frac{1}{3}+\frac{1}{4}) l\ A+(\frac{2}{3}+\frac{3}{4}) \ l\ W\)
a/w=(1/3+1/4)/(2/3+3/4)
a/w=((4+3)/12)/((8+9)/12)
A/W=7/17
the ratio of apple juice to water in this new mixture is 7 : 17.
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