Given a box contains a number of coins (pennies, dimes, and quarters)
The number of coins = 43
1 penny = 1 cent
1 dime = 10 cents
1 quarter = 25 cents
And the number of pennies = number of dimes = x
The number of quarters = y
So, x + x + y = 43
The total value of the coins = $3.34 = 334 cents
So, x + 10x + 25y = 334
So, we have the following system of equations;
[tex]\begin{gathered} 2x+y=43\rightarrow(1) \\ 11x+25y=334\rightarrow(2) \end{gathered}[/tex]From equation 1:
[tex]y=43-2x\rightarrow(3)[/tex]substitute from equation 3 into equation 2 to find x:
[tex]\begin{gathered} 11x+25(43-2x)=334 \\ 11x+25\cdot43-25\cdot2x=334 \\ 11x-50x+1075=334 \\ -39x=334-1075 \\ -39x=-741 \\ \\ x=\frac{-741}{-39}=19 \end{gathered}[/tex]substitute with x into equation 3 to find y:
[tex]y=43-2\cdot19=43-38=5[/tex]so, The number of pennies = 19
Number of dimes = 19
Number of quarters = 5
