SOLUTION: A teacher bought 100 puzzles for $82.90. She bought 3 types of puzzles. Type A cost 40 cents each, Type B costs 70 cents each, and Type C costs $1 each. How many more type C puzzle
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Question 513231: A teacher bought 100 puzzles for $82.90. She bought 3 types of puzzles. Type A cost 40 cents each, Type B costs 70 cents each, and Type C costs $1 each. How many more type C puzzles than type A puzzles did she buy?
I know it is not coins, but it is along the same path Answer by solver91311(24713) (Show Source):
You won't be able to determine the exact numbers of each type of puzzle because you only have enough information to create two equations where you are dealing with three variables. However, there is enough information to be able to determine the constant difference between C and A.
First you have the total amount of money expressed in dollars and then the price of two of the puzzle types expressed in cents. In order to get everything expressed in the same set of units AND to eliminate decimal fraction coefficients in the value equation, let's convert everything to cents. That means the total amount spent must be 8290 cents and the cost of a puzzle type C is 100 cents.
We are given that there were 100 puzzles altogether, so:
Then using the value data given, we can write a value equation:
Since we are concerned with the relative values of A and C, let's eliminate the variable B from the value equation. Solve the number equation for B:
And substitute:
A little Algebra music, Sammy:
Divide both sides by 30
Which is to say:
Which is what the questioner wanted to know.
John
My calculator said it, I believe it, that settles it
