Step-by-step explanation:
Let x be the number of 10 cent coins
Let y be the number of 20 cent coins
given
[tex]x = y + 12 \\ x - y = 12[/tex]
as equation 1
and
[tex]0.1x + 0.2y = 5.4[/tex]
as equation 2.
Now we will use elimination method to solve simultaneous equations.
Now we multiply equation 1 by 0.2 to eliminate y and solve for x first.
[tex]0.2 \times x - 0.2 \times y = 12 \times 0.2 \\ 0.2x - 0.2y = 2.4[/tex]
Let this new equation be equation 3.
Now use equation 2 + equation 3.
[tex]0.1x + 0.2x + (0.2y + ( - 0.2y)) = 5.4 + 2.4 \\ 0.3x = 7.8 \\ x = 7.8 \div 0.3 \\ = 26[/tex]
Substitute x into equation 1,
[tex]x = y + 12 \\ y + 12 = x \\ y = x - 12 \\ = 26 - 12 \\ = 14[/tex]
Therefore total number of coins = x + y = 26 + 14 = 40
