Question 1160362
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A boy has $3.70 in dimes and quarters. If the dimes were quarters, and the quarters were dimes, 
the money would have been $4.00. How many coins does the boy have? 
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From the condition, you have these two equations

    10d + 25q = 370       (1)

    25d + 10q = 400       (2)



Multiply equation (1) by 5 (both sides). Multiply equation (2) by 2  (both sides)

     50d +  125q = 1850    (3)

     50d +   20q =  800    (4)


Subtract equation (4) from equation (2)

           105q = 1850 - 800 = 1050.

             q            = 1050/105 = 10.


Then from equation (1),  d = (370-25*10)/10 = 12
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<U>ANSWER</U>.  &nbsp;&nbsp;There are 12 dimes and 10 quarters. The total number of coins is 22.


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Another way to find the total number of coins is to add equations (1) and (2).


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You will get then


    35d + 35q  = 370 + 400

    35*(d + q) = 770

    d + q = {{{770/35}}} = 22.
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