#### Understanding

Students consider ratio problems that involve an additional constraint on the quantities. In particular, the two quantities involved add to a given sum as well as have a proportional relationship. Students look at the problem using a table, a graph and equations.

### What to look for

Students might solve problems in this activity using double number lines, ratio tables, the unit rate, the equation, a graph, or drawing a diagram. The answers to the questions will vary. Ask students to note the advantages and disadvantages of using the various techniques.### Sample Assessment

A board is cut into two pieces in a ratio of 4:5. If the length of the board is 36 inches, how long is each piece?

Answer: 16 inches and 20 inches