Solve word problem

Question

If 2314 is the total amount of coins they have. How much of each coin do they have if A quarter times 2 is the amount of dimes, a quarter times 2 + 22 is the amount of nickels and the amount of nickels times 3 is the amount of pennys

Answer 1

p + n+d+q= 2314

2q=d

2q+22=n or q(2+22)=n?

3n=p

n=p/3

d+22=n=p/3

d=p/3-22

q=d/2=p/6-11

p+p/3+p/3-22+p/6-11=2314

11p/6= 2347

p=(6/11)(2347)= a non-integer

so, maybe 2314 =$23.14?

then 2314=p+5p/3+10p/3-220+25p/6-275

61p/6= 2809

p=(6/61)(2809)=another non-integer

that didn't work either

how about

2x25=50=d

2x25+22=72=n

3n=3x72=216=p

216+72+50+q=2314

q=2314-339=1975 quarters,

50 dimes, 72 nickels, 216 pennies

or

2q=d

q(2+22)=24q=n

3n=p

n=p/3

q=n/24=p/72

d=p/36

p+p/3+p/72+p/36=2314

99p/72=2314

p=(144/99)(2314)=another non-integer

try

p+5p/3+10p/36+25p/72=2314

242p/72=121p/36=2314

p=(36/121)(2314)=non-integer

the number of each coin has to be an integer