Let x be dimes and y be quarters
Julian has total of 24 coins so
x+y = 24 (1st equation)
Can be rewrite as y= 24-x
Total value is $4.5 so we need to change a dime or ten cents into $0.1 and a quarter into $0.25
So the second equation is
0.1 x + 0.25y = 4.5 substitute first equation into the second equation
0.1 x + 0.25 *(24-x) = 4.5 substitute y with (24-x)
0.1 x + 6 - 0.25x = 4.5
0.1 x - 0.25 x = 4.5 - 6 put all variables on the left side and the numbers on the right side
- 0.15 x = - 1.5 divide both side with - 0.15
x = 10
Numbers of dime is 10 coins
Proof
0.1 * 10 + 0.25 * 14 = $4.5
