SOLUTION: A student has 83 coins worth a total of $12.05. Each coin is either a Dime (10 cents) or a Quarter (25 cents). If x is the number of quarters, then x can be determined from the eq

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Question 892220: A student has 83 coins worth a total of $12.05. Each coin is either a Dime (10 cents) or a Quarter (25 cents). If x is the number of quarters, then x can be determined from the equation
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A student has 83 coins worth a total of $12.05.
Each coin is either a Dime (10 cents) or a Quarter (25 cents).
If x is the number of quarters, then x can be determined from the equation
:
Let y = no. of dimes
then
x + y = 83
and
.25x + .10y = 12.05
multiply the above equation by 10, subtract the 1st equation
2.5x + 1y = 120.50
x + y = 83
--------------subtraction eliminates y find x
1.5x = 37.5
x = 37.5/1.5
x = 25 quarters
:
;
To check this find the no. of quarter
y = 83 - 25
y = 58 dimes
Find the values
.25(25) + .10(58) =
6.25 + 5.80 = 12.05