Steve's doctor has advised him to take protein supplements. He bought two brands, Brand A and Brand B. The table gives the amoun
t of calcium, iron, and vitamins (in milligrams per spoonful) in each of the two brands. Brand Calcium Iron Vitamins A 5 4 7 B 4 6 4 Steve needs to take at least 24 milligrams of calcium, 15 milligrams of iron, and 16 milligrams of vitamins. Which ordered pairs of values are solutions for the given system inequalities, where x represents the number of spoonfuls of brand A that Steve takes and y represents the number of spoonfuls of brand B that Steve takes? Select all the correct answers. (1, 4) (1, 5) (2, 3) (3, 2) (4, 1)
I figured this out using each of the supplements one at a time. For calcium, Brand A gives you 5mg per spoon and Brand B gives you 4 mg per spoon. If you need 24 mg of calcium per day, divide 24 by each of those amounts per spoon. If you use Brand A, you need 24/5 = 4.8 (our first x value), and if you use Brand B, you need 24/4 = 6 (our first y value). Let's simplify that to (4, 6). That exists is a ratio of 2:3, so the x and y coordinates would be (2, 3) which is in fact a choice up above. Do the same for the Iron for A and B. 15mg needed/4mg per spoon in A = 3.75 (our second x value) and 15mg needed/6mg per spoon in B = 2.5 (our second y value). Simplify that down as well by rounding to (3, 2) which is also a choice. The last one, vitamins: 16mg needed/7mg per spoon in A = 2.2 (our last x value), and 16mg needed/4mg per spoon in B = 4 (our last y value). That can be rounded and simplified to a ratio of (1, 2) but that is not a choice. So... that's what I have! Hope it helps!
