Question

NEED HELP ASAPPP!!! Drag each scenario to show whether the final result will be greater than the original
value, less than the original value, or the same as the original value.

1. A $30 increase followed by a $30 decrease
2. A 20% decrease followed by a 40% increase
3. A 100% increase followed by a 50% decrease
4. A 75% increase followed by a 33% decrease
5. 55% decrease followed by a 25% increase
​

Answer 1

Answer:

Greater than the original = 2, 4

Less than the original = 5

Same as the original = 1, 3

Step-by-step explanation:

Let the original value be x.

1. A $30 increase followed by a $30 decrease.

New value $=x+30-30=x$, it is same as original value.

2. A 20% decrease followed by a 40% increase.

Afer 20% decrease.

New value $=x-\dfrac{20}{100}x=x-0.2x=0.8x$

Afer 40% increase.

New value $=0.8x+\dfrac{40}{100}(0.8x)=0.8x+0.32x=1.12x$, it is greater than original value.

Similarly check the other values.

3. A 100% increase followed by a 50% decrease.

New value $=x+\dfrac{100}{100}x-\dfrac{50}{100}(x+x)=x$, it is same as original value.

4. A 75% increase followed by a 33% decrease

New value $=x+\dfrac{75}{100}x-\dfrac{33}{100}(x+0.75x)=1.1725x$, it is greater than the original value.

5. 55% decrease followed by a 25% increase

New value $=x-\dfrac{55}{100}x+\dfrac{25}{100}(x-0.55x)=0.5625x$, it is less than the original value.

Therefore, Greater than the original = 2, 4, Less than the original = 5, Same as the original = 1, 3 .

Answer 2

Same As The Original:

A 100% increase followed by a 50% decrease

A $30 increase followed by a $30 decrease

Less Than The Original:

55% decrease followed by a 25% increase

Greater Than The Original:

A 20% decrease followed by a 40% increase

A 75% increase followed by a 33 1/3% decrease