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A.2.12.3 Meeting Constraints

You will now look at several situations that also involve two quantities and two constraints. Their job is to represent each pair of constraints by writing a system of equations and then to find a solution to the system.

This graph is available for your use when answering the following problems.

Here are some situations that each relates two quantities and involves two constraints. For each situation, find the pair of values that meet both constraints and explain or show your reasoning. A dining hall had a total of 25 tables—some long rectangular tables and some round ones. Long tables can seat 8 people. Round tables can seat 6 people. On a busy evening, all 190 seats at the tables are occupied.       How many long tables, x, and how many round tables, y, are there?

A family bought a total of 16 adult and child tickets to a magic show. Adult tickets are $10.50 each and child tickets are $7.50 each. The family paid a total of $141.           How many of adult tickets, x, and child tickets, y, did they buy?

At a poster shop, Han paid $16.80 for 2 large posters and 3 small posters of his favorite band. Kiran paid $14.15 for 1 large poster and 4 small posters of his favorite TV shows. Posters of the same size have the same price.