Question

A supermarket customer has paid a total of 156 l for 24 L of milk, 6 kg of Serrano ham and 12 L of olive oil. Calculate the price of each item, knowing that a liter of oil costs three times more than a liter of milk and that a kilogram of ham costs the same as buying 4 L of oil plus 4 L of milk.

Answer 1

Let x, y, z denote the costs of milk, Serrano ham, and olive oil, respectively. Form the related system of equations and solve.

`\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} 24x+6y+12z =156 \\ \ \qquad \qquad \quad \ z=3x \\ \qquad\ 4x+4z=y \end{matrix}\right.\ \Longrightarrow\ y=16x } \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf \bf{ 156=24x+6(16x)+12(3x)=156x\Longrightarrow x=1 } \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf \bf{ y= 16\qquad z=3 } \end{gathered}$}`

Milk costs 1 a liter, Serrano ham 16 a kilogram and olive oil 3 a liter.