Respuesta :
Answer:
Hence the System of equation are [tex]\left \{ {{x+y=12} \atop {0.1x+0.25y=2.25}} \right.[/tex]
There are 5 dimes and 7 quarters in my pocket.
Step-by-step explanation:
Let Number of dimes be 'x'.
Also Number of quarters be 'y'.
Now Given:
Total Number of Coins = 12
So the equation can be framed as;
[tex]x+y=12 \ \ \ \ equation \ 1[/tex]
Also Given:
Total Amount in pocket = $2.25
Now we know that 1 dime = $0.1
Also 1 quarter =$0.25
So the equation can be framed as;
[tex]0.1x+0.25y = 2.25 \ \ \ \ equation \ 2[/tex]
Hence the System of equation are [tex]\left \{ {{x+y=12} \atop {0.1x+0.25y=2.25}} \right.[/tex]
Now Solving the equation we get;
Now Multiplying equation 2 by 10 we get;
[tex]10(0.1x+0.25y)=2.25\times10\\\\10\times0.1x+10\times0.25y=22.5\\\\x+2.5y=22.5 \ \ \ \ equation\ 3[/tex]
Now Subtracting equation 1 from equation 3 we get;
[tex](x+2.5y)-(x+y)=22.5-12\\\\x+2.5y-x-y =10.5\\\\1.5y =10.5\\\\y= \frac{10.5}{1.5}= 7[/tex]
Now Substituting the value of y in equation 1 we get;
[tex]x+y=12\\\\x+7=12\\\\x=12-7 =5[/tex]
Hence there are 5 dimes and 7 quarters in my pocket.
