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A meal is made from three foods, with x, y and z portions.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A meal is made from three foods, with , and portions. The meal must have 10 portions in all. It must have 21 units of protein, where a portion of the foods has 2, 3 and 1 units. It must have 23 units of fibre, where a portion has 1, 2 and 4 units. So the equations are
Find the number of portions of each, and check the answer.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Put the coefficients in a matrix, one row for each equation, and the right sides in a vector.
Check. The answer is 3, 4 and 3 portions: , and . The determinant is 4, not zero, so the solution is the only one.
Answer: 3 portions of the first food, 4 of the second and 3 of the third.
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