gillian purchased 25 books at the library book sale. each hardcover book cost $1.50, and each paperback book…

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 $26.50. the book costs can be represented by the system of equations below.\n\n$h + p = 25$\n$1.50h + 0.50p = 26.50$\n\nhow many paperback books did gillian buy?\n11\n12\n13\n14

Answer

Explanation:

Step1: Solve the first - equation for h

From $h + p=25$, we get $h = 25 - p$.

Step2: Substitute h into the second - equation

Substitute $h = 25 - p$ into $1.50h+0.50p = 26.50$. $1.50(25 - p)+0.50p=26.50$. Expand the left - hand side: $37.5-1.50p + 0.50p=26.50$.

Step3: Combine like terms

Combine the p terms: $37.5-(1.50p - 0.50p)=26.50$, so $37.5 - p=26.50$.

Step4: Solve for p

Subtract 37.5 from both sides: $-p=26.50 - 37.5$, $-p=-11$. Multiply both sides by - 1: $p = 11$.