Question

Jenna spends $15.04 at the store on notebooks and folders for school. Notebooks cost $4.85 each, and folders cost $0.89 each. She buys a total of 8 items. Write and solve a system of equations to determine how many notebooks and how many folders Jenna bought.

Answer 1

Answer:

$\boxed{\text{2 notebooks and 6 folders}}$

Step-by-step explanation:

Let n = number of notebooks

and f = number of fodders

You have a system of two equations:

$\begin{cases}(1)& 4.85n + 0.89f = 15.04\\(2) & n+ f = 8\end{cases}$

$\begin{array}{lrcll}(3) & f & = & 8-n &\text{Subtracted n from each side of (2)}\\& 4.85n+0.89(8-n) & = & 15.04 &\text{Substituted (3) into (1)}\\& 4.85n+7.12-0.89n & = & 15.04 &\text{Distributed 0.89}\\& 3.96n+7.12 & = & 15.04 &\text{Combined like terms} \\& 3.96n & = & 7.92 & \text{Subtracted 7.12 from each side} \\(4) & n & = & 2 & \text{Divided each side by 3.96}\\& 2+ f & = & 8 & \text{Substituted (4) into (2)}\\& f & = & 6 &\text{Subtracted 2 from each side} \\\end{array}$

Jenna bought $\boxed{\textbf{two notebooks and six folders} }$.

Check:

$\begin{array}{rclcrcl}4.85\times2+0.89\times6 & =& 15.04 & \qquad &2+6&=&8\\9.70+5.34 & = & 15.04 & \qquad &8&=&8\\15.04& = & 15.04 & & & & \\\end{array}$

OK.