Kendra owns a toy store. She charges $8.00 for two puzzles and a piece of candy. She charges $4.50 for one puzzle and a piece of candy. How much does each puzzle cost?
A. $3.50
B. $4.50
C. $1.00
D. $2.25
Let's call the cost of a puzzle "x".
According to the problem, Kendra charges $8.00 for two puzzles and a piece of candy. This can be represented as:
2x + candy = $8.00
We don't know how much the piece of candy costs, but we can subtract the cost of it from both sides to isolate the variable:
2x = $8.00 - candy
Similarly, we can set up an equation for the cost of one puzzle and a piece of candy:
x + candy = $4.50
Again, we can subtract the cost of the candy from both sides:
x = $4.50 - candy
Now we have two equations for "x", both involving the unknown cost of the candy. However, we can use algebra to solve for "x" by eliminating the variable "candy".
Let's start by rearranging the first equation:
2x = $8.00 - candy
2x + candy = $8.00
Next, we can multiply the second equation by -2 to get -2x - 2candy = -$9.00:
-2(x + candy) = -$9.00
-2x - 2candy = -$9.00
Now we can add these two equations together, which eliminates the "candy" variable:
2x + candy = $8.00
-2x - 2candy = -$9.00
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0x - candy = -$1.00
So we have -candy = -$1.00, which means candy costs $1.00. Now we can substitute this value back into one of our original equations to solve for "x". Let's use the second equation:
x + candy = $4.50
x + $1.00 = $4.50
x = $3.50
Therefore, each puzzle costs $3.50.
The answer is A. $3.50