The total cost of 3 notebooks and 2 pens is ₹78, while the total cost of 5 notebooks and 4 pens is ₹138. Using Cramer's Rule, find the cost of one notebook and one pen.

Question

Accepted Answer

**Setting up the equations**

Let $x$ = cost of one notebook, $y$ = cost of one pen. The problem statement translates directly to
$$3x+2y=78$$
$$5x+4y=138$$

**Forming $D$**

$$D=\begin{vmatrix}3&2\5&4\end{vmatrix}=3(4)-2(5)=12-10=2$$

Since $D
eq0$, a unique solution exists.

**Forming $D_x$**

$$D_x=\begin{vmatrix}78&2\138&4\end{vmatrix}=78(4)-2(138)=312-276=36$$

**Forming $D_y$**

$$D_y=\begin{vmatrix}3&78\5&138\end{vmatrix}=3(138)-78(5)=414-390=24$$

**Solving**

$$x=\frac{36}{2}=18 \qquad y=\frac{24}{2}=12$$

So a notebook costs ₹18 and a pen costs ₹12. …

Q.The total cost of 3 notebooks and 2 pens is ₹78, while the total cost of 5 notebooks and 4 pens is ₹138. Using Cramer's Rule, find the cost of one notebook and one pen.

Concept understanding — Cramer's Rule for Two Linear Equations in Two Unknowns

Q.The total cost of 3 notebooks and 2 pens is ₹78, while the total cost of 5 notebooks and 4 pens is ₹138. Using Cramer's Rule, find the cost of one notebook and one pen.

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