Solving Book Distribution Problems: Word Problems and Equations
Word problems often involve sharing or distributing resources among individuals in a specific manner. In this article, we will solve two typical scenarios involving book distribution, which can be solved using basic algebraic equations and reasoning.
Problem 1: Donald and Dylan's Books
Donald and Dylan are roommates. Together they have one hundred eighty-eight books. If Donald has 34 books more than Dylan, how many does Dylan have?
We start by denoting the number of books Dylan has as (y) and the number of books Donald has as (g). The total number of books is 188:
(g y 188)
Donald has 34 more books than Dylan, so:
(g y 34)
Substituting (g) (y 34) into the first equation:
(y 34 y 188)
Simplifying the equation:
(2y 34 188)
Subtract 34 from both sides:
(2y 154)
Divide both sides by 2:
(y 77)
To find (g), we plug the value of (y) back into the original equation (g y 34):
(g 77 34 111)
Thus, Dylan has 77 books, and Donald has 111 books.
Problem 2: Kosumi and DeAndre's Books
Suppose Kosumi has (k) books and DeAndre has (d) books. Together they have 191 books. If Kosumi has 35 more books than DeAndre, how many books does each have?
Let (x) represent the number of books DeAndre has, and (y) the number of books Kosumi has. From the problem, we have:
(x (x 35) 191)
Simplifying:
(2x 35 191)
Subtract 35 from both sides:
(2x 156)
Divide both sides by 2:
(x 78)
Therefore, DeAndre has 78 books. Since Kosumi has 35 more books than DeAndre:
(y 78 35 113)
Thus, Kosumi has 113 books, and DeAndre has 78 books.
Conclusion
Both problems are typical word problems that can be solved using basic algebraic equations. By breaking down the problem into smaller, manageable parts, we can easily find the solution. This approach is not only effective but also helps in developing a systematic way of solving similar problems.