Step-by-step explanation:
d = number of dimes
n = number of nickels
p = number of pennies
d×$0.10 + n×$0.05 + p×$0.01 = $10.75
d = p/4
d = n × 2/3
now we need to transform these equation and substitute the variable equations in the main equation, so that we have actually only one variable left. and that we can solve.
so, it seems to me transforming p and n into expressions of d might be the easiest one.
d = p/4
=>
p = 4d
d = n × 2/3
=>
3d = 2n
n = d × 3/2
so, now putting that into the main equation
d×$0.10 + (d × 3/2)×$0.05 + 4d×$0.01 = $10.75
since we have a fraction in there, let's multiply everything by that denominator (2) to be fraction free :
2d×$0.10 + 3d×$0.05 + 8d×$0.01 = $21.50
now we can simplify the terms by multiplying the integer factors of d into the value decimals
d×0.20 + d×0.15 + d×0.08 = 21.50
now we can simply add up ask the factors of d
d×(0.2 + 0.15 + 0.08) = 21.50
d×0.43 = 21.50
d = 21.5 / 0.43 = 50
p = 4d = 4×50 = 200
n = d × 3/2 = 50 × 3/2 = 25 × 3 = 75
so he has 50 dimes, 75 nickels and 200 pennies
