Posted by john on Thursday, October 28, 2010 at 4:42pm.
1. Your prob. says sam has 23qtrs,but
I'm assuming you meant 23 coins; he can't have 23 qtrs if he only has 3.50.
x dimes, y qtrs,
Eq1: x + y = 23 coins,
0.10x + 0.25y = 3.50,
Multiply both sides by 20:
Eq2: 2x + 5y = 70.
Solve the 2 Eqs:
x + y = 23,
2x + 5y = 70,
Multiply the 1st Eq by -2:
-2x -2y = -46,
2x + 5y = 70,
Add the 2 Eqs:
3y = 24,
y = 8 Qtrs.
Substitute 8 for y in EQ1:
X + 8 = 23,
X = 23 - 8,
X = 15 Dimes.
2. Same procedure as prob. 1.