Posted by **john** on Thursday, October 28, 2010 at 4:42pm.

sam has $3.50 in dimes and quarters. he has 23 quarters all together. how many of each does he have?

will has $2.40 in dimes and nickels. he has 30 coins all together. how many of each does he have?

- ALgebra -
**Henry**, Saturday, October 30, 2010 at 1:40am
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.

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