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

 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

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

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

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

Hence explained.

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graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.