Question

gillian purchased 25 books at the library book sale. each hardcover book cost $1.50, and each paperback book cost $0.50. gillian spent a total of $26.50. the book costs can be represented by the system of equations below.
( h + p = 25 )
( 1.50h + 0.50p = 26.50 )
how many paperback books did gillian buy?
( \bigcirc ) 11
( \bigcirc ) 12
( \bigcirc ) 13
( \bigcirc ) 14

Explanation:

Step1: Solve for h from first equation

From \( h + p = 25 \), we get \( h = 25 - p \).

Step2: Substitute h into second equation

Substitute \( h = 25 - p \) into \( 1.50h + 0.50p = 26.50 \):
\[

$$\begin{align*} 1.50(25 - p) + 0.50p &= 26.50\\ 37.5 - 1.50p + 0.50p &= 26.50\\ 37.5 - p &= 26.50\\ -p &= 26.50 - 37.5\\ -p &= -11\\ p &= 11 \end{align*}$$

\]
Wait, that's not right. Wait, let's check again. Wait, 37.5 - p = 26.50, so -p = 26.50 - 37.5 = -11, so p = 11? But wait, let's recalculate. Wait, 1.5025 is 37.5. Then 37.5 -1.5p +0.5p = 37.5 -p. Set equal to 26.5. So 37.5 -26.5 = p. 37.5 -26.5 is 11? Wait, no, 37.5 -26.5 is 11? Wait, 37.5 -26.5 = 11? Yes. So p = 11? But the options have 11 as an option. Wait, but let's check with the equations. If p=11, then h=14. Then 1.514 +0.5*11 = 21 +5.5=26.5. Yes, that's correct. So the answer is 11.

Answer:

11