Clodagh tests the knowledge of her two younger sisters, Anna and Lauren - Junior Cycle Mathematics - Question 12 - 2013

Anna could have set up an equation based on the statement:

Let the number be $x$. Then, the equation would be:

$8 + 3x = 47$

To solve for $x$:

1. Subtract 8 from both sides:

   $3x = 47 - 8$

o $3x = 39$

2. Divide by 3:

   $x = \frac{39}{3}$

   $x = 13$

This shows that Anna's calculated number is indeed 13.

To solve the simultaneous equations:

1. From the first equation: $5x + 2y = 30 \implies 2y = 30 - 5x$

   This simplifies to:

   $y = 15 - \frac{5}{2}x$

2. Now substitute $y$ in the second equation:

   $3x - 2(15 - \frac{5}{2}x) = 2$

   Expanding gives:

   $3x - 30 + 5x = 2$

   $(3x + 5x) - 30 = 2\implies 8x = 32 \implies x = 4$

3. Now substitute $x = 4$ back into one of the original equations to find $y$:

   $5(4) + 2y = 30 \implies 20 + 2y = 30 \implies 2y = 10 \implies y = 5$

4. Therefore, the solution to the simultaneous equations is: $x = 4, y = 5$