"A person has quartes(25ct), dimes(10ct.), nickels(5ct), and pennies(1ct), with a total value of $3.86. The number of nickels is twice the number of quarters. The number of quarters is two less than the number of dimes. There are 40 coins altogether. Write and solve an equation to find the number of each coin."
I already came to the equation 3.86=x*0.05+(1/2)x*0.25+((1/2)*x+2)*0.10+y*0.01 and 40-x-y=0, but the numbers for the coins are real numbers.
Can someone help me find a right equation and solve it?
+23245 Let the number of dimes be: d
Then, since the number of quarters is two less than the number of dimes: q = d - 2
The number of nickels is twice the number of quarters: n = 2·q = 2(d - 2) = 2d - 4
Since there are 40 coins, p + n + d + q = 40
or: p + (2d - 4) + d + (d - 2) = 40
Solving for p: p + 4d - 6 = 40 ---> p = 46 - 4d
.01(46 - 4d) + .05(2d - 4) + .10(d) + .25(d - 2) = 3.86
Multiply by 100:
(46 - 4d) + (10d - 20) + (10d) + (25d - 50) = 386
41d - 24 = 386
41d = 410
---> d = 10
Use this to find the other answers and check the work.
+23245 Let the number of dimes be: d
Then, since the number of quarters is two less than the number of dimes: q = d - 2
The number of nickels is twice the number of quarters: n = 2·q = 2(d - 2) = 2d - 4
Since there are 40 coins, p + n + d + q = 40
or: p + (2d - 4) + d + (d - 2) = 40
Solving for p: p + 4d - 6 = 40 ---> p = 46 - 4d
.01(46 - 4d) + .05(2d - 4) + .10(d) + .25(d - 2) = 3.86
Multiply by 100:
(46 - 4d) + (10d - 20) + (10d) + (25d - 50) = 386
41d - 24 = 386
41d = 410
---> d = 10
Use this to find the other answers and check the work.
