The owner of a restaurant orders replacement knives, forks, and spoons.

Question

The owner of a restaurant orders replacement knives, forks, and spoons. A package arrives with 40 utensils weighing exactly 141.3 oz (excluding the weight of the box). Each knife, fork, and spoon weigh 3.9 oz, 3.6 oz, and 3.0 oz, respectively.
(a) How many solutions are there to the number of knives, forks, and spoons?
(b) What is the maximum number of spoons?
(c) What is the minimum number of spoons?

Answer 1

Let # of spoons = x

Let # of forks = y

Let # of knives = z

 

Then we have the equation

 

x + y + z = 40                                eq1

3x + 3.6y + 3.9z = 140                   eq2

 

This is one solution.

 

If we change the variables so that spoons is y, forks is z, and knives is y.  We can alter the second equation to get a second solution.

 

 

spoons = x , y , z

forks =    y , z , x

knives = z , x , y

 

Given this arrangement, you will have a maximum of 3 solutions.