8.2.4 Ratios in Food and Drink
Activity: Using Ratios in Food and Drink
(a) A fruit drink has to be diluted by mixing 1 ounce of the concentrate with 5 ounces of water. How much water should be added to 4 ounces of concentrate? How much drink will this make?
Have you considered drawing a sketch of a glass with ounces marked along its side?
(a) The ratio of concentrate to water is 1:5, so five times as much water as concentrate is required. If 4 ounces of concentrate is used, of water is needed. If 4 ounces of concentrate and 20 ounces of water are used, the amount of drink will be .
(b) The ratio of white flour to wholemeal flour in a bread recipe is 3:7. If 6 ounces of white flour is used, how much wholemeal flour is needed? Can you explain why this is called a “70% wholemeal loaf”?
Because the ratio is 3:7, this means 6 ounces of white flour is equivalent to 3 parts. How much is 1 part of white flour?
[ Alternatively, you could use the corresponding fraction and find an equivalent fraction where the numerator is 6 (because there are 6 ounces of white flour). ]
(b) The resulting denominator would be your answer.
If 3 parts are equivalent to 6 ounces, one part is equivalent to . 7 parts are equivalent to . Thus, 14 ounces of wholemeal flour are needed.
There are 10 parts altogether, and 7 parts are wholemeal, so the fraction of the flour that is wholemeal is or 70%; hence the name.
Notice that there are different ways of tackling these problems and sketches might help you to understand the situation better.