SOLUTION: The value of a number of dimes and quarters is $1.25. If the number of dimes was doubled and the number of quarters was increased by 5, the value would be $3.00. How many dimes a

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: The value of a number of dimes and quarters is $1.25. If the number of dimes was doubled and the number of quarters was increased by 5, the value would be $3.00. How many dimes a      Log On


   

Question 1107720: The value of a number of dimes and quarters is $1.25. If the number of dimes was
doubled and the number of quarters was increased by 5, the value would be $3.00.
How many dimes and quarters are there?
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Work with the description literally, and simplify the system from that and you should obtain a system, d for dimes and q for how many quarters:
system%282d%2B5q=25%2C4d%2B5q=35%29
which you can solve without a doubt.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Josgarithetic above gave the correct system of equations but gave no 
explanation as to how he got them.
The value of a number of dimes and quarters is $1.25.
0.10D + 0.25Q = 1.25
If the number of dimes was doubled and the number of quarters was increased by 5, the value would be $3.00.
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%282D%2B5Q=25%2C4D%2B5Q=35%29

You'll get 5 dimes and 3 quarters.

Edwin