need a help with this problem since it lacks info (dinner rolls & max calories)

[atlmixcoatl]

if a small dinner roll has 59 calories and a large dinner has 79 calories, what is the maximum total calories from these items that could NOT be eaten by all the dinner guests combined?

That's all the question states.

the way i broke it down was: 59 x 79 =4661 -138 =4523, but i'm not sure if this is correct since the word problem itself lacks info.

 

[ksdhart2]

The problem has enough information to solve it, although it's definitely not an easy task. In general, problems of this sort involve finding the Frobeniu numbers for a given set of integers. In this case, you want to find the largest possible integer that cannot be written as a sum of some integer multiples of 59 and 79. In other words, you want to find the largest integer b such that \(\displaystyle 59x + 79y = b\) has no solution for integers x and y.

For instance, the dinner guests could eat just one small roll and no large rolls. Then the total calories eaten would be 59(1) + 79(0) = 59. Or they could eat twelve small rolls and five large rolls, giving 59(12) + 79(5) = 1103 calories. What other calorie totals can you make? What calorie totals can you not make? What do you think the largest such calorie total would be?

Incidentally, your given answer is correct, although I don't know enough about the topic to know if your reasoning is sound or not. You can find some information on ways people have tackled this problem. I looked up "algorithms to find Frobenius numbers" and found these two pages: Stack Overflow and Math Stack Exchange. Perhaps you can find others you like better.