Jillian is selling boxes of cookies to raise money for her basketball team. The 10 oz. box costs $3.50, while the 16 oz. box costs $5.00. At the end of one week, she collected $97.50, selling a total of 24 boxes. The system of equations that models her sales is below. x+ y= 24 3.50x + 5.00y = 97.50 Solve the system of equations. How many 10 oz. boxes were sold?
a. 6
b. 9
c. 12
d. 15
x + y = 24 <=> x = 24 - y. So far we have the value of x relative to the value of y. Now we can replace it in the second equation: 3.5x + 5y = 97.5 <=> 3.5 * (24 - y) + 5y = 97.5 <=> 84 - 3.5y + 5y = 97.5 <=> 1.5y = 97.5 - 84 <=> 1.5y = 13.5 <=> y = 13.5/1.5 <=> y = 9. And since x was 24 - y, this means that x = 15. So the answer is D.
