Respuesta :
Step 1
Given the equation that represents the situation as;
[tex]\begin{gathered} 5x+2y=20 \\ \text{where x represents the number of hardcover books} \\ y\text{ represents the number of paperback books} \end{gathered}[/tex]Required; Find the possible combination of books Derek can buy based on the options
Step 2
Test the options
[tex]\begin{gathered} A\text{. 5x+2y=20} \\ 5(-2)+2(15)=20 \\ -10+30=20 \\ 20=20 \\ \text{ we have 20= 20.} \\ \text{But Derek cannot have -2 hardcover books} \\ \text{Therefore, option A is wrong.} \end{gathered}[/tex][tex]\begin{gathered} B)\text{ (0,10)} \\ 5(0)+2(10)=0+20=20 \\ \text{This will mean that Derek will buy only paperback books} \\ \text{This does not suggest a combination. } \\ \text{Therefore, we will not work with option B} \end{gathered}[/tex][tex]\begin{gathered} C(2,5) \\ 5(2)+2(5)=10+10=20 \\ \text{This looks like a possible combination} \\ \text{Option C is right.} \end{gathered}[/tex][tex]\begin{gathered} D(3,\frac{5}{2}) \\ \text{Derek cannot buy }\frac{5}{2}\text{ of a paperback books} \\ \text{Therefore, option D is wrong too} \end{gathered}[/tex]Answer; Option C (2,5). That is 2 hardcover books and 5 paperback books
