Question

a. In the cafeteria, there is one large 10-seat table and many smaller 4-seat tables. Thereare enough tables to fit 200 students. Write an inequality whose solution is the possiblenumber of 4-seat tables in the cafeteria.b. 5 barrels catch rainwater in the schoolyard. Four barrels are the same size, and theAfth barrel holds 10 liters of water. Combined, the 5 barrels can hold at least 200 litersof water. Write an inequality whose solution is the possible size of each of the 4barrels.c. How are these two problems similar? How are they different? Solve ach problem.

Answer 1

According to the statement given in Part a, there is one table for 10 people and many tables for 4 and in total there are tables for 200 people. Taking x as the number of tables for 4 people, the inequality that represents this situation is:

`\begin{gathered} 4x+10\leq200 \\ 4x\leq190 \\ x\leq47.5 \end{gathered}`

It means that there must be less than or 47.5 tables in the cafeteria.

According to the statement given in Part b, there are 4 barrels that are the same size, and one that is 10 liters, in total they can hold 200 liters. Taking x as the volume hold by the 4 barrels , the inequality that represents this situation is:

`\begin{gathered} 4x+10\leq200 \\ 4x\leq190 \\ x\leq47.5 \end{gathered}`

It means that each barrel must hold less than or 47.5 liters of water.

These problems are similar because of the inequality used to find the solution is the same, they are different because of the variable that is found is completely different, the first one is the number of tables and the second one is the volume that can be hold by the barrels.