A.2.5.2 Snacks in Bulk

To get snacks for a class trip, Clare went to the “bulk” section of the grocery store, where she could buy any quantity of a product and the prices are usually good. Clare purchased some salted almonds at $6 a pound and some dried figs at $9 per pound. She spent $75 before tax. If she bought 2 pounds of almonds, how many pounds of figs did she buy?

If she bought 1 pound of figs, how many pounds of almonds did she buy?

Write an equation that describes the relationship between pounds of figs and pounds of almonds that Clare bought, and the dollar amount that she paid. Be sure to specify what the variables represent.

Here is a graph that represents the quantities in this situation. Choose any point on the line, state it's coordinates, and explain what it tells us.

Choose any point that is not on the line, state its coordinates, and explain what it tells us.

From the graph, it looks like (7, 3.5) might be a solution, but it is hard to know for sure. Is there a way to verify?

Suppose we extend the two ends of the graph beyond the first quadrant. Would a point on those parts of the line — say, (-1, 9) — be a solution to the equation 6a + 9f = 75? Why or why not?"