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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?

Nov 27, 2019

#1
+106533
+2

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

Nov 27, 2019
edited by CPhill  Nov 27, 2019

#1
+106533
+2

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

CPhill Nov 27, 2019
edited by CPhill  Nov 27, 2019
#2
+8810
+1

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.

!

Nov 27, 2019
edited by asinus  Nov 27, 2019
edited by asinus  Nov 27, 2019
edited by asinus  Nov 27, 2019