Question

Benjamin has a total of two hundred fifty-eight coins. He has three times as many nickels as pennies and one-half as many pennies as quarters. How much money does he have?

Answer 1

p+n+q = 258
n = 3p
q = 2p
so
p + 3p + 2p = 258
he has 43 pennies
now finish it off

Answer 2

let x be the no. of pennies
let y be the no. of nickels
let x be the no. of quarters
x + y + z = 258 —> Eq. 1
y = 3x —> Eq. 2
x = 1/2z —> Eq 3.
Solution: substitute y = 3x to Eq. 1
x + y + z = 258
x + 3x + z = 258
4x + z = 258
Substitute x = 1/2z to
4(1/2z) + z = 248
2z + z = 258
3z = 258 ; z = 86 quarters
x = 1/2 (86)
x = 43 pennies
y = 3 (43)
y = 129 nickels
Total Money = 0.01x + 0.05y + 0.25z
= 0.01 (43) + 0.05 (129) + 0.25 (86)
Total Money = $28.38