Aj bought a portable game system on sale for $150.the portable game system was 70% of the regular price.aj concluded that the original price of the portable game system must have been $225.

Aj correct? justify your answers
part b
is 70% of an original price the same 30% of an original price explain

.7 * 225 = 157.50 so no

no
70% of original is 30% OFF original

To determine whether Aj is correct in concluding that the original price of the portable game system was $225, we can use the concept of finding a part of a whole.

Let's break down the information given:

1. Aj bought the portable game system on sale for $150.
2. The portable game system was 70% of the regular price.

To find the original price of the portable game system, we need to calculate the whole amount based on the given percentage.

Step 1: Set up a proportion:

Let "x" be the original price.
We have: $150 (sale price) is to x (original price) as 70% (fraction) is to 100% (whole).

Step 2: Convert the percentage to a decimal:

70% = 70/100 = 0.70

Step 3: Set up the proportion:

$150/x = 0.70/1

Step 4: Solve for x:

x = ($150 * 1) / 0.70 = $214.29 (approximately)

Therefore, based on the calculations, the original price of the portable game system should be approximately $214.29, not $225.

Now, moving on to part b:

To understand if 70% of an original price is the same as 30% of an original price, we can compare the two percentages.

Let "x" be the original price.

For 70% of the original price, we calculate it as:

70% = 70/100 * x

For 30% of the original price, we calculate it as:

30% = 30/100 * x

Comparing these two expressions, we can see that they are different because the percentages being multiplied are different. Hence, 70% of an original price is not the same as 30% of an original price.