Question

The bookstore ordered 15 Sociology work books and 10 Economy 101 textbooks on August 1st to prepare for the fall semester. After realizing they miscounted, the bookstore order 1 more Sociology workbook and three more Economy 101 textbooks on August 15th. If August 1st the order was for $4300 and the August 15th order was $800 , find the cost of one Sociology workbook and one Economy 101 textbook?

Answer 1

e = number of books on Economy
s = number of books on Sociology

so the order on August 1st looks like 15s + 10e = 4300
and the order on August 15th looks like 1s + 3e = 800


`\bf \begin{array}{lllll} 15s&+&10e&=&4300\\ s&+&3e&=&800 \end{array}\\\\ -------------------------------\\\\ \boxed{s}=800-3e\qquad thus \\\\\\ 15s+10e=4300\implies 15\left( \boxed{800-3e} \right)+10e=4300\qquad then \\\\\\ 12000-45e+10e=4300\implies 12000-4300=45e-10e \\\\\\ 7700=35e\implies \cfrac{7700}{35}=e\implies \boxed{220=e} \\\\\\ now \qquad s+3e=800\implies s+3(220)=800\implies s=800-660 \\\\\\ \boxed{s=140}`