The quarters, buckled, and dimes totaled 20 and their value was $2.05. How many kind were there if there were 3 times as many dimes as quarters
Accepted Solution
A:
We assume the question is intended to say there are a total of 20 quarters, nickels, and dimes, the value of which is $2.05. The number of dimes is 3 times the number of quarters.
Let q, n, d represent the numbers of quarters, nickels, and dimes, respectively. Then you have three equations in the unknowns: q +n +d = 20 25q +5n +10d = 205 -3q +d = 0
A calculator can give the solution to this matrix equation in short order. It is q = 3 n = 8 d = 9
There are 3 quarters, 8 nickels, and 9 dimes.
_____ If you use the third equation to write an expression for d, you can substitute that into the other two equations. q +n +3q = 20 25q +5n +10(3q) = 205 Simplifying, these are 4q +n = 20 11q +n = 41 Subtracting the first from the second, we find 7q = 21 q = 3 From there, it is easy to find d=9, n=8.