SOLUTION: Hello all, I am struggling with the following problem. I know it is probably really easy and im just not understanding something, but I keep getting stuck on how to express the var

Question 290924: Hello all, I am struggling with the following problem. I know it is probably really easy and im just not understanding something, but I keep getting stuck on how to express the variable for calculating the amount of each coin and there $ value in each equation. Any help will be great.
A jar contains 100 coins made up of 50 cent coins and 20 cent coins. How many coins are there if the total value of the coins is $38.00. Solve algebraically.
a) Express this problem as a system of two equations. Define variables correctly.
b) Solve system of equations simultaneously.
Thanks, -Nick.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A jar contains 100 coins made up of 50 cent coins and 20 cent coins. How many coins are there if the total value of the coins is $38.00. Solve algebraically.
a) Express this problem as a system of two equations. Define variables correctly.
Quantity Eq:::: f + t = 100
Value Eq::::: 50f + 20t = 3800 cents
---------
b) Solve system of equations simultaneously.
Multiply thru the 1st Eq by 20:
20f + 20t = 20*100
50f + 20t = 3800
-----------------------
Subtract 1st from 2nd and solve for "f":
30f = 1800
f = 60 (# of first cent coins)
---
Since f + t = 100, t = 40 (# of twenty cent coins)
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Cheers,
Stan H.
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