Question 5

We will form a linear equation based on the given information and solve it.

Step 1 — Formulating the equation

Let's assume the number of five-rupee coins. Let the number of five-rupee coins be $\mathbf{x}$. Ruby has 3 times as many two-rupee coins. So, the number of two-rupee coins is $\mathbf{3x}$. The value from five-rupee coins is $5 \times x$. The value from two-rupee coins is $2 \times 3x$. The total value of all coins is ₹88. We can write an equation for the total value.

$5x + 2(3x) = 88$

$5x + 6x = 88$

$11x = 88$

$x = \frac{88}{11}$

$\boxed{x = 8}$

Step 2 — Finding the number of coins

We found the value of $\mathbf{x}$ in the previous step. The number of five-rupee coins is $\mathbf{x}$.

$\text{Number of five-rupee coins} = 8$

The number of two-rupee coins is $\mathbf{3x}$.

$\text{Number of two-rupee coins} = 3 \times 8$

$\text{Number of two-rupee coins} = 24$

Answer

(i) Number of five-rupee coins = 8 (ii) Number of two-rupee coins = 24