Final answer:
The equation representing all the ways Caleb could spend his $100 on corn and wheat, given that corn costs $20 per pound and wheat costs $4 per pound, is 20x + 4y = 100. This equation illustrates his budget constraint and the trade-off between buying pounds of corn and wheat with his limited funds.
Step-by-step explanation:
To answer the student's question, we will need to create a budget constraint equation that represents all the ways Caleb could spend his $100 on corn and wheat, with the given prices.
Given that corn costs $20 per pound and wheat costs $4 per pound, and that x represents the number of pounds of corn that Caleb purchases and y represents the number of pounds of wheat, the equation to determine all possible combinations of corn and wheat that add up to $100 can be expressed as:
20x + 4y = 100
This equation implies that for every pound of corn represented by x, Caleb will spend $20, and for every pound of wheat represented by y, he will spend $4.
To visualize Caleb's options, one could graph this equation on a coordinate plane where the x-axis represents pounds of corn and the y-axis represents pounds of wheat. The line that results from this equation represents all possible combinations of corn and wheat that Caleb could purchase with his $100.
For example, if Caleb decides to buy 5 pounds of corn (x=5), that would cost him $100, and he would have no money left for wheat (y=0). Conversely, if he were to spend all of his money on wheat, he could buy 25 pounds of wheat (y=25), resulting in no corn purchased (x=0). Any combination on the line between these two points is also a possible solution for Caleb's budget spending.