Final answer:
The question asks for the calculation of the number of cookies Barney started with, the number he ate, and the weight gain associated with cookie consumption, using the conversion rate of 20 cookies per 1 pound gained. Without provided values for the cookies, no exact number can be given, but the relationship between cookie consumption and weight gain can be established through the proportion Y/20, where Y represents the number of cookies eaten.
Step-by-step explanation:
The student's question pertains to a scenario involving Barney and a bag of cookies. Without specific numbers provided for the quantity of cookies Barney started with or consumed, it is not possible to calculate the exact number of cookies or the resultant weight gain directly. However, the problem seems to suggest an understanding of proportionality and unit conversion, specifically how many pounds are gained per quantity of cookies consumed.
If we assume Barney started with X cookies and ate Y of them, for every 20 cookies eaten, he would gain 1 pound. Therefore, if Barney ate all X cookies, the weight he would gain can be calculated by the formula: Weight gained (in pounds) = Y/20.
The question appears to be related to unit conversions and basic algebraic calculations. For instance, similar to how one might calculate conversions between miles and feet, pounds and ounces, tons and pounds, cups and ounces, quarts and pints, or quarts and gallons in various other example problems provided.