Exercise 42 Page 377

We are told that a farmer grows corn c, tomatoes t, and sunflowers s. We know that he wants to plant twice as many acres of tomatoes as acres of sunflowers. This can be written as the following equation. t=2s Additionally, we are told that he wants to plant 40 more acres of corn than of tomatoes, which can be written as an equation as well. c=40+tWith the two equations, we can write the following System of Equations. t=2s & (I) c=40+t & (II) We are also told that the farm has 320 acres. Therefore, we can write and rearrange the following equation. t+s+c=320 ⇔ t=320-s-c As the t-variable is isolated, we are going to substitute its equivalent expression into Equation (I) and Equation (II) so that our system will only have two unknowns.

Now that the equations are simplified, we can solve the system using the Substitution Method. To do so, we will need to isolate the s-variable in Equation (II).

Next, the s-variable's equivalent expression can be substituted in Equation (I).

We found that c=152. Finally, we can solve for s by substituting 152 for c in Equation (II).

The solution for our system of equations is c=152 and s=56. This means that the farmer should plant 152 acres of corn and 56 acres of sunflowers. The last thing we need to do is find the number of acres of tomatoes. We can use the fact that the farm has 320 acres. t+152+56=320 ⇔ t=112 Therefore, the farmer should plant 112 acres of tomatoes.