Mathnasium Word Problem: Quack!

It's a quack-tastic Word Problem Wednesday! Check your answer below.

Three loaves of stale bread is enough to feed 8 adult ducks or 16 ducklings. How many loaves of bread are needed to feed 6 adult ducks and 12 ducklings?

The humane society recommends limiting the amount of bread fed to birds. Like humans, birds will do well with a wide variety of foods, and stuffing them with bread (except perhaps your Thanksgiving turkey) will limit their intake of nutritional foods. This is especially true of ducklings that need high grade nutrients to develop properly. Given that birds move about freely and you have no control over their diet, my inclination is that if you want to provide food, then provide food that is nutritionally appropriate in your backyard where they can feed safely, and you can enjoy their company.

This problem is an exercise in proportions. It’s a little more challenging because we’re scaling down rather than scaling up, and fractions are involved. Regardless, a method that I’ve found approachable is to talk through the solution.

4 ducks need 3 loaves of bread.
Hence, 1 duck needs a ¼ of the 3 loaves bread, or ¾ of a loaf.
Hence, 3 ducks need 3 of ¾ of a loaf or 9/4 = 2¼ loaves.
8 ducklings need 3 loaves of bread.

Hence 1 duckling needs ⅛ of the 3 loaves of bread, or ⅜ of a loaf.
Hence, 6 ducklings need 6 of ⅜ of a loaf or 18/8 = 2¼ loaves also!
Together, the 3 ducks and 6 ducklings need 2¼ + 2¼ = 4½ loaves.

Using the standard proportion (fraction) method would require transliterating the problem into an equation:
3 loaves per 4 ducks = X loaves per 3 ducks; or 3/4 = X/3 and solving for X. This will result in the arithmetic above in the talk through solution: X = ¾ x 3 = 9/4 = 2¼ loaves. Likewise, for ducklings, 3/8 = X/6 => X = 3/8 x 6 = 2¼ loaves.

Hence, a total of 4½ loaves. Personally, since bread is not the best food for ducks and may do them harm, I think it should be kept as human food. I would turn the loaves into a refreshing Panzanella salad, followed by a scrumptious meatloaf entree, and finished with a delicious bread pudding dessert! A wonderful meal that I would enjoy except that I’m gluten sensitive and that meal would do me harm!

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