MEDAL AWARD. You have a total of 25 coins, all nickels and quarters. The total value is $3.85. How many of each type of coin do you have? Use a system of linear equations to solve. Use substitution or elimination. Show all work.

Question

***[isuru]*** · Answer

the first thing is
      20 nickels = $1
        4 quarters = $ 1

so... lets assume that u have "x" amount of nickels and "y" amount of quarters. since u have only 25 coins in your hand
                 x + y = 25 
and this is the first equation.

now  moving to the second data given.. the sum of money u have is $3.85
  which means the total value of coins  you got is $3.85
     if  you got 1 nickel u will have - >$ 1/20  = $ 0.05
     if  u got "x" amount of nickel u will have -> x times  $ 0.05 = 0.05(x)
in the same way
     if  u have 1 quarter you will have - > $ 1/4 = $ 0.25 
     if  u got "y" amount of quarters you will have -> y times $ 0.25 = 0.25(y)

but the total is $3.85 which means
        0.05(x) + 0.25(y) = 3.85
multiply the whole equation by 100 and u will get
         5x + 25y = 385 

so the system of equatio u have is
          5x + 25y = 385
           x + y = 25
now i think u can solve this for x and y .. and its all left to do :)

whpalmer4 · Answer

I usually find it easiest to write coin problems in terms of cents from the outset:

$$n+q = 25$$$$5n+25q = 3.85*100$$
I would probably solve this by multiplying the first equation by -5, then adding the two together:

$$-5n-5q=-125$$$$~5n+25q = ~~~385$$-----------------
$$-5n+5n-5q+25q=-125+385$$You should be able to do the rest...

anonymous · Answer

Why do you multiply the first equation by -5?

***[isuru]*** · Answer

that way when u add the first equation to the second one the term "5n" gets cancel out...

the first equation have (-5n) since it was multiplied by (-5)
the second equation already have (5n)

add them together 
 -5n + 5n = 0

so the only unknown variable remaining is "q" ... so u have a linear equation with 1 unknown term.. which is easy to solve :)

anonymous · Answer

So 13 quarters?

anonymous · Answer

And 12 nickels?

whpalmer4 · Answer

Yes, easily checked:

13*25 = 325
12*5 = 60
325+60 = 385

And thanks for the explanation, ISURU!

anonymous · Answer

Okay thank you both!