Final answer:
Mr. Thompson's original savings was $4,800, calculated by setting up an equation based on him spending $1,600 on a TV and 2/3 of the remainder on a refrigerator and being left with 1/3 of his original savings.
Step-by-step explanation:
Mr. Thompson's original savings can be determined using algebraic methods based on the information given in the problem. We know that after spending $1,600 on a television set, he spent 2/3 of the remainder on a refrigerator and was left with 1/3 of the original amount of savings. Let's define the original amount of savings as 'x'.
After spending $1,600, the remainder is 'x - 1,600'. Since 2/3 of this remainder was spent on a refrigerator, the amount used for the refrigerator is 2/3 (x - 1,600). This leaves him with 1/3 of the original amount, which is 1/3 x.
The equation can be set up as follows:
x - 1,600 - 2/3 (x - 1,600) = 1/3 x
Now, we solve for 'x' to find Mr. Thompson's original savings.
Multiply both sides by 3 to eliminate the fraction:
3(x - 1,600) - 2(x - 1,600) = x
This simplifies to:
3x - 4,800 - 2x + 3,200 = x
Combining like terms gives us:
x - 1,600 = x
which further simplifies to:
x = 4,800
Therefore, Mr. Thompson's original savings was $4,800.