Question

You have dimes and quarters in your pocket. There are 12 coins that total $2.25. Write and solve a system of linear equations to find the number of dimes and the number of quarters

Answer 1

Answer:

Hence the System of equation are $\left \{ {{x+y=12} \atop {0.1x+0.25y=2.25}} \right.$

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;

$x+y=12 \ \ \ \ equation \ 1$

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;

$0.1x+0.25y = 2.25 \ \ \ \ equation \ 2$

Hence the System of equation are $\left \{ {{x+y=12} \atop {0.1x+0.25y=2.25}} \right.$

Now Solving the equation we get;

Now Multiplying equation 2 by 10 we get;

$10(0.1x+0.25y)=2.25\times10\\\\10\times0.1x+10\times0.25y=22.5\\\\x+2.5y=22.5 \ \ \ \ equation\ 3$

Now Subtracting equation 1 from equation 3 we get;

$(x+2.5y)-(x+y)=22.5-12\\\\x+2.5y-x-y =10.5\\\\1.5y =10.5\\\\y= \frac{10.5}{1.5}= 7$

Now Substituting the value of y in equation 1 we get;

$x+y=12\\\\x+7=12\\\\x=12-7 =5$

Hence there are 5 dimes and 7 quarters in my pocket.