Mrs Lee went shopping at a departmental store. She spent 1/5 of her money on a TV set and $800 on a washing machine. Then, she spent 1/8 of the remaining amount on a refrigerator. After which, the amount of money left was $200 more than half of the amount she had at first. How much money did she had at first?

Question

Mrs Lee went shopping at a departmental store. She spent 1/5 of her money on a TV set and $800 on a washing machine. Then, she spent 1/8 of the remaining amount on a refrigerator. After which, the amount of money left was $200 more than half of the amount she had at first. How much money did she had at first?

Answer 1

Let's start by setting up an equation to represent the information given:

Amount Mrs Lee had at first - 1/5 * amount - $800 - 1/8 * (amount - 1/5 * amount - $800) = 1/2 * amount + $200

Simplifying this equation, we get:

4/5 * amount - $800 - 1/8 * (4/5 * amount - $800) = 1/2 * amount + $200

Multiplying both sides by 40 to get rid of fractions, we get:

32 * amount - 3200 - 5 * (4 * amount - 800) = 20 * amount + 8000

Simplifying this equation, we get:

32 * amount - 3200 - 20 * amount + 4000 = 20 * amount + 8000

12 * amount = 17200

Amount Mrs Lee had at first = $1,433.33 (rounded to the nearest cent)

Therefore, Mrs Lee had $1,433.33 at first.

Answer 2

Let's assume that Mrs Lee had x amount of money at first.

She spent 1/5 of her money on a TV set, which is (1/5)x.
She also spent $800 on a washing machine.

After these two purchases, the remaining amount of money is x - (1/5)x - $800.

Then, she spent 1/8 of the remaining amount on a refrigerator, which is (1/8) * (x - (1/5)x - $800).

After this purchase, the amount of money left was $200 more than half of the amount she had at first, which can be expressed as:

x - (1/5)x - $800 - (1/8) * (x - (1/5)x - $800) = (1/2)x + $200

Now, let's solve this equation to find the value of x.

x - (1/5)x - $800 - (1/8) * (x - (1/5)x - $800) = (1/2)x + $200

Multiply through by 40 to get rid of the fractions:

40x - 8x - 32000 - 5(x - (1/5)x - $800) = 20x + 8000

Simplify the equation:

32x - 32000 - 5(x - (1/5)x - $800) = 20x + 8000

32x - 32000 - 5(x - 1/5 * x - $800) = 20x + 8000

32x - 32000 - 5(4/5 * x - $800) = 20x + 8000

32x - 32000 - 4x + $4000 = 20x + 8000

Combine like terms:

28x - 28000 = 20x + 8000

Subtract 20x from both sides:

8x - 28000 = 8000

Add 28000 to both sides:

8x = 36000

Divide by 8:

x = 4500

Therefore, Mrs Lee had $4500 at first.