Question 215332
Jody has a collection of 116 coins consisting of dimes, quarters, and silver dollars. the number of quarters is 5 less than three-fourths of the number of dimes. The number of the silver dollars is 7 more than five-eighths of the number of dimes. How many coins of each kind are in her collection?


Step 1.  Let {{{x}}} be the number of dimes.


Step 2.  Let {{{3x/4-5}}} be the number of quarters since number of quarters is 5 less then three-fourths of the number of dimes


Step 3.  Let {{{5x/8+7}}} be the number of silver dollars since number of the silver dollars is 7 more than five-eighths of the number of dimes


Step 4.  Then, {{{x+3x/4-5+5x/8+7=116}}} since Jody has a collection of 116 coins consisting of dimes, quarters, and silver dollars.


Step 5.  Simplify the equation in Step 4.


{{{x+3x/4-5+5x/8+7=116}}}


Multiply 24 to both sides of the equation to get rid of denominators.


{{{24*(x+3x/4-5+5x/8+7)=24*116}}}


{{{24x+18x-120+15x+168=2784}}}


{{{57x+48=2784}}}


{{{57x=2784-48=2736}}}


{{{57x/57=2736/57}}}


{{{x=48}}}


With {{{x=48}}}, then {{{3x/4-5=3*48/4-5=31}}} and  {{{5x/8+7=5*48/8+7=37}}}


Check total number of coins:  48+31+37=116 which is a true statement.


Step 6.  The number of dimes is 31, the number of quarter is 31 and the number of silver dollars is 37.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J