1550.12 – Malaz, Ron, Debra, and Sabrina

Malaz, Ron, Debra, and Sabrina are celebrating their third consecutive snow day. They have $47 to spend on party supplies. Unfortunately, the roads are unsafe, so they must purchase everything from the shop on the ground floor of their apartment building. Each of them will get part of the $47 to spend. To make this a more interesting problem for you, the problem solver, you are now being told that Malaz and Ron together have $27, Malaz and Debra have $25, and Malaz and Sabrina have $23. How much money does each person get?

Solution

Malaz gets $14. Ron gets $13. Debra gets $11. Sabrina gets $9.

One way to solve this problem is:

$M + R + D + S = 47.$

But $M + R = 27$ , $M + D = 25$ , and $M + S = 23$ .

Substituting $R$ , $D$ , and $S$ in terms of $M$ and simplifying, $2M = 28$ , so $M = 14$ , and so on.

BUT: for students who do not have a grip on algebra, here is a nice question that can lead to the solution without using algebra.

Notice that $27 + 25 + 23 = 75$ , which is not $47$ – why not?

Someone will notice that Malaz's share has been included 3 times, so $75 - 47 = 28$ must equal the 2 extra Malaz shares.

The solution follows along...