Question 217473
question #16

The total value of the dimes and quarters in a coin bank is $3.70. If the dimes were quarters and the quarters were dimes, the total value of the coins would be $2.95. find the number of quarters in the coin bank.


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


Step 2.  Let {{{y}}} be the number of quarters.


Step 3.  Let {{{0.10x}}}  be the dollar value of dimes.


Step 4.  Let {{{0.25y}}}  be the dollar value of quarters.


Step 5.  Then, {{{0.10x+0.25y=3.70}}}   since the total value of the dimes and quarters in a coin bank is $3.70. 


Step 6.  Then {{{0.10y+0.25x=2.95}}}  since the dimes were quarters and the quarters were dimes, the total value of the coins would be $2.95


Step 7.   Based on Steps 5 and 6 we have the following linear system of equations which will  be solved by elimination.


{{{0.10x+0.25y=3.70}}} 
{{{0.25x+0.10y=2.95}}} 


Step 8.  Let's get rid of the decimal point by multiplying both equations by 100.


{{{10x+25y=370}}}   Equation A
{{{25x+10y=295}}}   Equation B


Step 9.  Multiply Equation A by  by {{{2/5}}}  to both equations to simplify the problem a bit.


{{{(10x)*(2/5)+25*(2/5)=370*(2/5)}}}


{{{4x+10y=148}}}  Equation A1
{{{25x+10y=295}}} Equation B


Step 10.  Subtract Equation A1 from Equation B to get the following:


{{{(25-4)x+(10-10)y=295-148}}} 


{{{21x=147}}} 


Step 11.  Divide {{{11}}}  to both sides of the equation


{{{21x/21=147/21}}} 


{{{x=7}}} 


Step 12.Substitute {{{x=7}}}  into {{{4x+10y=148}}}  to find y


{{{4*7+10y=148}}} 


{{{28+10y=148}}} 


Step 13.  Subtract {{{28}}}  from both sides of the equation


{{{28+21y-28=148-28}}} 


{{{10y=120}}} 


Step 14.  Divide by {{{10}}}  to both sides of the equation.


{{{10y/10=120/10}}} 


{{{y=12}}} 


Step 15.  Now check if {{{x=7}}}  and {{{y=12}}}  satisfies  Equation B or {{{25x+10y=295}}}


{{{25*7+10*12=175+120=295}}} which is a true statement.


Step 16.  ANSWER:  In the coin bank there are 7 dimes and 12 quarters.


I hope the above steps and explanation were helpful.


For free Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry, please visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Also,  good luck in your future studies. 


Respectfully,
Dr J