This week’s Mitzvah Math lesson is related to Purim since it is soon here.
Our Sages taught that the Jews faced the horrible decree of Haman because they lacked unity and were not always kind and giving to each other. That’s why the Megillah teaches about the mitzvot of matanot l’evyonim (gifts to the poor) and mishloach manot (sending food to friends). The matanot l’evyonim are meant to help those in most need of help. The mishloach manot are meant to build up the quality of our friendships.
We like to travel around town to deliver mishloach manot, but the Rambam teaches that caring for the poor should be our top priority. Here is what he teaches in Mishneh Torah, Megillat Esther 2:17—“One should rather spend more money on gifts to the poor than on his Purim banquet and presents to his friends. No joy is greater and more glorious than the joy of gladdening the hearts of the poor, the orphans, the widows, and the strangers.”
Here is a math problem related to that: Say you have $60 total to spend on matanot l’evyonim and mishloach manot and you want to prioritize matanot l’evyonim. You decide you want to give $26 more to matanot l’evyonim than mishloach manot. How much would you be giving to each one?
Solution: A problem like this can be a little tricky because it’s easy to think about it in the wrong way. If you know some algebra, I encourage you to try to solve this problem that way. I’m going to take a general approach.
I’m going to use a strategy professional mathematicians often use when solving math problems. So if you like math already or want a glimpse into that world, this is a great opportunity.
The strategy works like this. We don’t know the answer right away but we do know that it needs to be some “shift” away from a balanced state where both matanot l’evyonim and mishloach manot are equal to each other. Therefore, we’ll experiment a bit. That is, after we start with everything balanced then we will add a little to the matanot l’evyonim. But this also means that we need to take away something from mishloach manot because we only have $60 to spend. If we keep experimenting, we should see a pattern and then get the answer we want.
Therefore, let’s start with matanot l’evyonim and mishloach manot both equal to each other. In this case that means they would both be $30 because the total amount, that is $60, divided by 2 is $30. Now let’s see what happens when we add $5 to the matanot l’evyonim and also $10 to matanot l’evyonim. We can make a chart to track things:
Total $ | matanot l’evyonim | remaining money for mishloach manot | difference between matanot l’evyonim and mishloach manot
Balanced
60 | 30 | 30 | 0
$5 added to matanot l’evyonim
60 | 35 | 25 |10
$10 added to matanot l’evyonim
60 | 40 | 20 | 20
Can you see the connection between the difference of matanot l’evyonim and mishloach manot and the amount we added? A difference of 10 resulted from adding $5 and a difference of 20 resulted from adding $10. If that pattern is true in general that the difference is always twice what we add on to matanot l’evyonim.
The original problem asks for the amounts of matanot l’evyonim and mishloach manot when the difference is $26. That means that we need to add half that, that is $13, to matanot l’evyonim when the two payments start in a balanced state of $30 each. Therefore, matanot l’evyonim is $30 + $13 = $43 and mishloach manot is the remaining $60 – $43 = $17. Shabbat Shalom.
Ari Blinder is a math educator living in Highland Park, New Jersey. He is the owner of Math for the Masses, an innovative tutoring and consulting company. Please visit www.math4masses.com for fun activities and helpful worksheets. Ari can be reached at [email protected]. Never think you are “not a math person.” You are very much one already, but no one has shown you how.