SOLUTION: how do I solve the following:
Your Change jar contains only dimes and quarters. If you took it to the bank and the bank's coin machine indicated it contained 82 coins valued at
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Your Change jar contains only dimes and quarters. If you took it to the bank and the bank's coin machine indicated it contained 82 coins valued at
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Question 189863This question is from textbook Begining Algebra once and for all
: how do I solve the following:
Your Change jar contains only dimes and quarters. If you took it to the bank and the bank's coin machine indicated it contained 82 coins valued at $13, how many of each coin was in the jar? Make a table and try different values for the numner of each/and or use an equation This question is from textbook Begining Algebra once and for all
Let d be the number of dimes and let q be the number of quarters. Then:
The total amount of money is $13. It will be convenient to represent this as 1300 cents. Since there are d dimes and each of them is worth 10 cents, the total value of all of the dimes is 10d cents. Likewise the total value of all of the quarters is 25q cents. Since there were only dimes and quarters in the change jar, the value of the dimes plus the value of the quarters must equal the total amount of money in the jar, so:
But since
We can also say:
Having an expression for the quantity q in terms of d allows us to make the following substitution:
Solve the equation for d to determine the number of dimes, then subtract the number of dimes from 82 to determine the number of quarters.
