SAT Mathematics Practice Test 5

Let n be the number of novels and m be the number of magazines that Sadie purchased. If Sadie purchased a total of $\\$11$novels and magazines, then$n+m=11.$It is given that the combined price of 11 novels and magazines is$\$20$. Since each novel sells for $\\$4$and each magazine sells for$\$1$,it follows that $4n+m=20.$ So the system of equations below must hold$4n+m=20$

$n+m=11$Subtracting side by side the second equation from the first equation yields $3n=9$, so $n=3$. Therefore, Sadie purchased 3 novels.Choice A is incorrect. If 2 novels were purchased, then a total of $\\$8$was spent on novels. That leaves$\$12$ to be spent on magazines, which means that $12$ magazines would have been purchased. However, Sadie purchased a total of $11$ novels and magazines. Choices C and D are incorrect. If $4$ novels were purchased, then a total of $\\$16$dollars was spent on novels. That leaves$\$4$ to be spent on magazines, which means that $4$ magazines would have been purchased. By the same logic, if Sadie purchased 5 novels, she would have no money at all ($\\$0$) to buy magazines. However, Sadie purchased a total of 11 novels and magazines.