Question

Peter takes 5 minutes to make a sandwich and 10 minutes to make dumplings. If he plans tospend no more than 1 hour making food, what inequality represents the number of sandwichesand dumplings Peter can make? What is the graph of the solution set?

Answer 1

Let x be the number of sandwiches Peter makes and let y be the number of dumplingshe makes.

Since he takes 5 minutes per sandwich, the total time he uses to make them is

$5x$

The total times he uses to make dumplings is

$10y$

The total time he spends preparing food is the sum of the two things, that is

$5x+10y$

He wants to spend no more than an hour to make the food, this means the time he is willing to spend making food is less or equal to 60 minutes. (We have to put the hour in minutes, so that the units are the same). Then the inequality representing the number and sandwiches that Peter can make in that time is

$5x+10y\leq60$

To graph the solution set for this inequality we first graph the line that represents this situation, that is, the line

$5x+10y=60$

whose graph is