SOLUTION: Peter is playing poker. He cashes out 3 red chips and 4 blue chips for 23 dollars, and 5 red chips and 12 blue chips for 65 dollars. How many dollars is each red chip worth?

Question 973243: Peter is playing poker. He cashes out 3 red chips and 4 blue chips for 23 dollars, and 5 red chips and 12 blue chips for 65 dollars. How many dollars is each red chip worth?
Found 2 solutions by algebrahouse.com, josmiceli:
Answer by algebrahouse.com(1659) (Show Source): You can put this solution on YOUR website!
r = worth of red chip
b = worth of blue chip

3r + 4b = 23 {3 red chips and 4 blue chips for $23}
5r + 12b = 65 {5 red chips and 12 blue chips for $65}

-9r - 12b = -69 {multiplied top equation by -3}
5r + 12b = 65 {bottom equation stays the same}
--------------
-4r = -4 {added the two equations}
r = 1 {divided each side by -4}

3r + 4b = 23 {top equation}
3(1) + 4b = 23 {substituted 1 for r into top equation}
3 + 4b = 23 {multiplied}
4b = 20 {subtracted 3 from each side}
b = 5 {divided each side by 4}

red chip is worth $1
blue chip is worth $5

For more help from me, visit: www.algebrahouse.com

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the cash value of 1 red chip
Let = the cash value of 1 blue chip
-----------------
given:
(1)
(2)
----------------------
Multiply both sides of (1) by and
subtract (2) from (1)
(1)
(2)
------------------------

Each red chip is worth $1
------------------------
check:
(1)
(1)
(1)
(1)
-------------------
(2)
(2)
(2)
(2)
OK

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