Question

Part ADerek has $20 to spend on used books. Hardcover books cost $5 each and paperbacks cost $2 each. Complete the equation which determines the number x of hardcover books and the number y of paperback books he can buy.Answer:5x+2y=20Part BFor the situation in Item 14, which of the following represents a possible combination of books that Derek can buy? Select all that apply.A.(–2, 15)B.(0, 10)C.(2, 5)D.(3,5/2)

Answer 1

Step 1

Given the equation that represents the situation as;

`\begin{gathered} 5x+2y=20 \\ \text{where x represents the number of hardcover books} \\ y\text{ represents the number of paperback books} \end{gathered}`

Required; Find the possible combination of books Derek can buy based on the options

Step 2

Test the options

`\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}`
`\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}`
`\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}`
`\begin{gathered} D(3,(5)/(2)) \\ \text{Derek cannot buy }(5)/(2)\text{ of a paperback books} \\ \text{Therefore, option D is wrong too} \end{gathered}`

Answer; Option C (2,5). That is 2 hardcover books and 5 paperback books