Chapter 7.4, Problem 7P

A company mixes fertilizer and soil in a 4 to 9 ratio by weight, but the amounts of fertilizer and soil the company mixes vary. Let F be an unspecified number of pounds of fertilizer, which can vary, and let S be the corresponding number of pounds of soil the company might use. For each of the following equations and math drawings, discuss whether or not the equation is correct. If it is, explain how to reason about quantities and use a math drawing to obtain the equation. If the equation is not correct, explain why not and discuss how a student might come up with it.

1. $S=9.F.$ See Figure 7.33.

 

Figure 7.33 Critique or explain the equation and math drawing.

$9.S=4.F.$ See Figure 7.34.

 

Figure 7.34 Critique or explain the equation and math drawing.

$\frac{1}{9}.S=\frac{1}{4}.F.$ See Figure 7.35.

 

Figure 7.35 Critique or explain the equation and math drawing.