Respuesta :
Given:
The number of coins =30.
The total value of the coins in the jar is $ 4.70.
We know that quarter is worth 25 cents, nickels is worth 5 cents and a dollar is worth 100 cents.
Let x be the number of coins of the quarter.
The value of quarter =25x.
Let y be the number of coins of the nickles.
The value of nickels =5y.
[tex]\text{ The number of coins =x+y=30}[/tex][tex]x+y=30[/tex][tex]x=30-y[/tex]Conver the dollar into cents by multiplying 100, we get
[tex]\text{ \$4.70=4.70}\times100[/tex][tex]\text{ \$4.70=47}0\text{ cents}[/tex][tex]\text{The value of the coins in jar = 25x+5y=470}[/tex][tex]25x+5y=470[/tex]Substitute x=30-y in this equation to find the value of y.
[tex]25(30-y)+5y=470[/tex][tex]750-25y+5y=470[/tex][tex]750-20y=470[/tex]Subtracting 750 from both sides, we get
[tex]750-20y-750=470-750[/tex][tex]-20y=-280[/tex]Dividing both sides by (-2), we get
[tex]-\frac{20y}{-20}=-\frac{280}{20}[/tex][tex]y=14[/tex]Substitute y=14 in x=30-y to find the value of x.
[tex]x=30-14=16[/tex]We get x=16.
Hence the number of coins of the quaters = 16 and the number of coins of the nickels =14.
