Question

Half of an orange juice mixture is orange concentrate. Explain why the ratio of orange concentrate to water is 1 : 1.

Answer 1

Answer: The explanation is given below.

Step-by-step explanation: Given that half of an orange juice mixture is orange concentrate.

We are to explain the reason behind the ratio of orange concentrate to water being 1 : 1.

Let x be the quantity of the total orange juice mixture.

Then, according to the given information, the orange concentrate in the mixture will be

`q_o=(1)/(2)* x=(x)/(2).`

The rest of the mixture will be water, of course. The quantity of water in the mixture will be

`q_w=x-(x)/(2)=(x)/(2).`

Therefore, the ratio of orange concentrate to water is given by

`r=q_o:q_w=(x)/(2):(x)/(2)=((x)/(2))/((x)/(2))=(1)/(1)=1:1.`

Thus, the ratio of orange concentrate to water is 1 : 1.

Hence explained.