Mr. thomas spent $1,600 of his savings on a television set and 2/5 of the remainder on a refrigerator. he had 1/3 of his original amount of savings left. a) what was mr. thomas's original savings? b) what was the cost of the refrigerator?

a) $3,600    b) $800

Step-by-step explanation:

a)

He had originally x amount of money.

He spent $1600 on a TV.

Now he has x - 1600.

Then he spent 2/5 of the remainder on a fridge.

He spent 2/5(x - 1600) on the fridge.

Finally he has 1/3 of x left.

original amount - TV money - fridge money = (1/3)x

x - 1600 - (2/5)(x - 1600) = (1/3)x

Multiply both sides by the LCM of the denominators: 3 * 5 = 15

15[x - 1600 - (2/5)(x - 1600)] = 15[(1/3)x]

15x - 15(1600) - (15)(2/5)(x - 1600) = 5x

15x - 24,000 - 6x - 9600 = 5x

9x - 14,400 = 5x

4x = 14,400

x = 3,600

His original savings was $3600.

b)

He started with $3,600.

He spent $1,600 on the TV. Now he has $3,600 - $1,600 = $2000.

He spent 2/5 of the remainder in the fridge. 2/5 * $2,000 = $800

The fridge cost $800.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

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step-by-step explanation: