Question 720341: Ok So I Have A Question From Math Class That Says: I Have A Mason Jar Full Of Coins, Your Task Is To Calculate Exactly How Many Pennies, Nickles, Dimes And Quarters Are In The Jar. There Are Exactly 513 Coins In The Jar, The Combined Weight Of The Jar And The Coins Is 1779 Grams, The Number Of Pennies In The Jar Is Twice The Sum Of The Nickels, Quarters And Dimes.
I Was Allowed To Ask 3 Questions I Asked The Weight Of The Jar. The Jar Weighs 301 Grams By Itself. I Also Asked How Much Each Coin Ways And He Said Pennies Weigh 2.5 Grams, Nickels Weigh 5 Grams, Quarters Weigh 5.8 Grams, And Dimes Weigh 2.3 Grams. I Then Asked What The Total Amount Of Money In The Jar Was And He Said There Is $17.12
Please Help Me Figure This Out I Can't Seem To Get The Right Answer
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! I will help you set of the system of equations. But then I will leave it up to you to solve it.
- There are four unknowns:
Let p = the number of pennies
Let n = the number of nickels
Let d = the number of dimes
Let q = the number of quarters - With four unknowns we will need a system of four equations to solve the problem.
- Since there are 513 coins altogether:
p + n + d + q = 513 - Since the number of pennies is twice the sum of nickels, dimes and quarters:
p = 2*(n + d + q)
or
p = 2n + 2d + 2q - Since the weight of everything is 1779 grams and the weight of the jar is 301, the weight of all the coins is 1779 - 301 = 1478 grams.
- Since each penny weighs 2.5g, "p" pennies would weigh 2.5p grams. Since each nickel weighs 5g, "n" nickels would weigh 5n grams. Since each dime weighs 2.3g, "d" dimes would weigh 2.3d grams. Since each quarter weighs 5.8g, "q" pennies would weigh 5.8q grams. And finally, since all the coins together weigh 1478 grams:
2.5p + 5n + 2.3d + 5.8q = 1478
If you don't want to work with decimals, you can multiply both sides by 10:
25p + 50n + 23d + 58q = 14780
- The final equation will deal the the values of these coins. To make things easier (IMHO), I am going to use values expressed in terms of cents instead of dollars. So instead of the total value being $17.12 I will use 1712 cents. Each penny is worth 1 cent so p pennies will be worth p cents. Each nickel is worth 5 cents so n nickels will be worth 5n cents. Each dime is worth 10 cents so d dimes will be worth 10d cents. Each quarter is worth 25 cents so q quarters will be worth 25q cents. So
p + 5n + 10d + 25q = 1712
If you'd rather work with dollars, this equation would be:
0.01p + 0.05n + 0.10d + 0.25q = 17.12
So the system of equations that will lead to a solution will be:
p + n + d + q = 513
p = 2*(n + d + q) or p = 2n + 2d + 2q
2.5p + 5n + 2.3d + 5.8q = 1478 or 25p + 50n + 23d + 58q = 14780
p + 5n + 10d + 25q = 1712 or 0.01p + 0.05n + 0.10d + 0.25q = 17.12
Many methods can be used to solve such a solution, including:- Substitution
- Linear combination (aka elimination, aka addition)
- Several matrix-based methods (Gaussian elimination, inverse matrices, etc.)
- Determinants/Cramer's Rule
I'll leave it up to you to choose a method of solution and find the solution.
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