James (Jim) Frankenfield - Problem of the Day/Week/Month

Current Math or Physics Problem

I will be posting a "daily" problem here. Well, maybe weekly or monthly or irregularly. There may be a hint here as well, if you open that heading. The problem may be posted on facebook groups as well. In that case somebody may post the solution before you attempt it, although it may or may not be correct. When a new problem is posted the solution to the last will be posted here and then archived.

The type of problem and difficulty will vary from high school through calculus. If the current one is too easy or too hard for you check back for the next one and it may be more your style/level.

Current Problem:

One ounce of secret burger sauce A at McJim's has ingredients a and b in a ratio of 4:3 (4 parts a and 3 parts b). One ounce of McFrank's secret sauce B has the same ingredients, a and b, in a ratio of 1:2. You discover that mixing the two sauces in a ratio of 3:5 (3 parts A and 5 parts B) tastes better than either by itself. If you mix up a large batch of your new sauce of 1680 ounces how many ounces each of ingredients a and b will be in it?

Hints:

As stated you know A has 4/7 oz a and 3/7 oz b. And similarly for B but in thirds. But this is not very intuitive to work with and fractions can be avoided up front. The LCM (Least Common Multiple) is 21 - how many ounces of a and of b are in 21oz of A? How about B? Now you can mix them and keep track of ounces of each ingredient.

You can also work directly with the fractions and get improper fractions for a and for b after mixing. Rather than reduce or use the fractions directly consider their ratio. The LCM of 21 will still show up in your calculations this way as well.

There are often multiple ways to view a problem and to solve it so you, or somebody else, may find an alternate approach as well.