Judd paid 182 dollars for a thermos, a blender, and a microwave. The blender cost 35 more dollars than the thermos. the microwave cost 65.50 more than a blender. Find the cost of the blender? please show your work.
Let t = thermos
t + t + 35 + t + 35 + 65.50 = 182
3t + 135.5 = 182
3t = 46.50
t = 15.50
blender = 15.5 + 35
To find the cost of the blender, we can set up a system of equations based on the given information.
Let's say the cost of the thermos is x dollars. According to the problem, the blender costs $35 more than the thermos, so its cost would be x + $35. Additionally, the microwave costs $65.50 more than the blender, meaning its cost is (x + $35) + $65.50.
Now we can add up the prices of all three items to set up an equation:
x + (x + $35) + ((x + $35) + $65.50) = $182.
Simplifying this equation gives:
x + x + $35 + x + $35 + $65.50 = $182.
Combining like terms yields:
3x + $135.50 = $182.
Next, we want to isolate the variable, so we'll subtract $135.50 from both sides:
3x = $182 - $135.50.
Simplifying this equation gives:
3x = $46.50.
Finally, we divide both sides of the equation by 3 to solve for x:
x = $46.50 / 3.
Evaluating this division gives:
x = $15.50.
Therefore, the cost of the thermos is $15.50.
Since the problem states that the blender costs $35 more than the thermos, we can calculate its cost by adding $35 to the cost of the thermos:
Blender cost = $15.50 + $35 = $50.50.
Hence, the cost of the blender is $50.50.