April 2021
Problem of the Month

Place Setting Problem

A knife weighs as much as two spoons.

Three spoons weigh as much as a knife and a fork.

A plate weighs as much as a knife and a spoon.

A fork weighs four ounces.

How much does the spoon weigh?
How much does the knife weigh?
How much does the plate weigh?

Solution to the Problem:

The spoon weighs 4 ounces, the knife weighs 8 ounces, and the plate weighs 12 ounces.

Let s = weight of the spoon
Let f = weight of the fork
Let k = weight of the knife
Let p = weight of the plate

Then write the equations:
k = 2s
3s = k + f
p = k + s
f = 4

Subsituting equations 1 and 4 into equation 2, we get 3s = 2s + 4
So s = 4
Therefore, k = 2s = 2(4) = 8
And finally, p = 8 + 4 = 12

Correctly solved by:

1. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
2. Ivy Joseph	Pune, Maharashtra, India
3. Taylor Balding	Redlands Middle School, Grand Junction, Colorado
4. Noell Kaiser	Mountain View High School, Mountain View, Wyoming
5. Anna T. Vice	Landon School, Bethesda, Maryland

Send any comments or questions to: David Pleacher