Question 1100753: You have a jar containing 74 coins, consisting entirely of pennies and quarters, worth a total of $6.74. How many quarters are in the jar?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
x = number of pennies
y = number of quarters
x+y = total number of coins
x+y = 74 is the first equation. Solving for y gets us y = 74-x (subtract x from both sides)
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1 penny = 0.01 dollars
x pennies = 0.01x dollars (multiply both sides by x)
1 quarter = 0.25 dollars
y quarters = 0.25y dollars (multiply both sides by y)
0.01x+0.25y = total value of money
0.01x+0.25y = 6.74 is the second equation
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The system of equations is
y = 74-x
0.01x+0.25y = 6.74
Plug the first equation into the second, then solve for x
0.01x+0.25y = 6.74
0.01x+0.25(y) = 6.74
0.01x+0.25(74-x) = 6.74 ... y has been replaced with 74-x
0.01x+0.25(74)+0.25(-x) = 6.74
0.01x+18.50-0.25x = 6.74
-0.24x+18.50 = 6.74
-0.24x+18.50-18.50 = 6.74-18.50
-0.24x = -11.76
-0.24x/(-0.24) = -11.76/(-0.24)
x = 49
Use this value to find y
y = 74-x
y = 74-49
y = 25
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In summary, x = 49 and y = 25 meaning there are 49 pennies and 25 quarters
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