a vending machine contained $13 in dimes and quarters. There were 70 coins. How many dimes did the vending machhine contain?

Let x be the number of dimes

Then, 70 - x  = number of quarters

And

Number of dimes x their value  + Number of quarters x their value  = Total Value

x * .10    +    (70 - x) .25    =   13        simplify

.10x   + 17.5 - .25x   = 13

-.15x + 17.5  =    13       subtract 17/5 from both sides

-.15x  =  -4.5           divide both sides by -.15

x = 30  =  number of dimes  .....   and there are 40 quarters

Check

30 (.10)   +  40(.25)  =

3  +  10     =  13

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