Phineas and Ferb are preparing to conduct experiments at Dataknee Incorporated. Phineas bought 4 beakers and 3 goggles for $33. Ferb bought 6 beakers and 2 goggles for $32. How much did each beaker and each goggle cost?

This system of equations problem can be resolved with elimination or substitution. It is determined from the calculations that the cost of a beaker (X) is $3, and the cost of a goggle (Y) is $7.

Explanation:

This question is essentially asking you to solve a system of linear equations, where the cost of a beaker is one variable and the cost of a goggle is another variable. From the problem, we can formulate two equations.
Let X be the cost of a beaker and Y be the cost of a goggle. Thus, from Phineas, we get the equation: 4X + 3Y = $33. From Ferb, we get the equation: 6X + 2Y = $32. Now, we can solve this system by either substitution or elimination.
For this problem, let's use elimination. We will multiply the first equation by 2 and the second one by 3 to make the Y coefficients equal, then we can subtract one equation from the other.
We get: 8X + 6Y = $66, and 18X + 6Y = $96. Subtracting the first from the second, we get: 18X - 8X = $96 - $66, or 10X = $30, thus X = $3 (cost of a beaker).
We then substitute X = $3 in either of the two initial equations to find Y. Substituting in the first one, we get: $12 + 3Y = $33, or 3Y = $21, thus Y = $7 (cost of a goggle).

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