Question 1107720
<pre>Josgarithetic above gave the correct system of equations but gave no 
explanation as to how he got them.</pre>The value of a number of dimes and quarters is $1.25.<pre>0.10D + 0.25Q = 1.25</pre>If the number of dimes was doubled and the number of quarters was increased by 5, the value would be $3.00.<pre>0.10(2D) + 0.25(Q+5) = 3.00

Simplify each equation:

0.10D + 0.25Q = 1.25  <-- move decimals two places right
    10D + 25Q = 125   <-- divide through by 5
      2D + 5Q = 25

0.10(2D) + 0.25(Q+5) = 3.00  <--move decimals two places right
    10(2D) + 25(Q+5) = 300   <--divide through by 5
      2(2D) + 5(Q+5) = 60    <--simplify
        4D + 5Q + 25 = 60    <--subtract 25 from both sides
             4D + 5Q = 35   
              
Solve the system of equations:

{{{system(2D+5Q=25,4D+5Q=35)}}}

You'll get 5 dimes and 3 quarters.

Edwin</pre>