Percent word problem

[crunchberries]

Problem: When the local department store put all of its shirts on sale for 20% off, Jason saved a total of $30 by purchasing four shirts. What was the total price of the four shirts before the sale?


So here's what I know. 20% off is the same as 20/100 or .2. We're looking for the total price of four shirts, but we don't know what one shirt costs. So we can represent the cost of one shirt as x. So four shirts is 4x

or... or something. Honestly, I have no clue what I'm doing. It's been so long since I've gone to school and I really want to get into an algebra class, but these 2 step word problems kill me every time. I have such difficulty breaking them down despite knowing how to calculate percentages (like 40% of 400 is 160, if Stacy won 8 out of 20 games, she won 40% of her games, etc.)

 

[Quaid]

Hi.

Yes, the decimal form of 20% is 0.2. Therefore, if we desire to calculate 20% of some number, we multiply that number by 0.2

The question does not ask about individual shirt prices (plus, the shirts likely have different prices, so we don't have enough information to determine individual shirt prices, anyway).

The question wants to know what the total was for those four shirts before subtracting 20% off for the sale.

Let x = the pre-sale total for the four shirts

The store calculated 20% of x, and the result was a $30 savings.

Are you good to finish it?

Cheers

 

[crunchberries]

Hi.

Yes, the decimal form of 20% is 0.2. Therefore, if we desire to calculate 20% of some number, we multiply that number by 0.2

The question does not ask about individual shirt prices (plus, the shirts likely have different prices, so we don't have enough information to determine individual shirt prices, anyway).

The question wants to know what the total was for those four shirts before subtracting 20% off for the sale.

Let x = the pre-sale total for the four shirts

The store calculated 20% of x, and the result was a $30 savings.

Are you good to finish it?

Cheers

I think I got it.

20% of x is 30

so 20x = 30

20x/20 = 30/20

x= 30/20 or 3/2

3 divided by 2 = 1.5

1.5 X 100 = 150

So the 4 shirts were $150.

 

[Quaid]

I think I got it.

20% of x is 30

so 20x = 30

Not quite true (as you can see, if you substitute x=150).


The following are correct equations.

0.2x = 30

(20/100)x = 30

30 divided by 0.2 (aka 20/100 aka 1/5) is 150

:cool:

Also, do you know? Dividing by a ratio is the same as multiplying by its reciprocal.

In other words:

0.2x = 30

(1/5)x = 30

x = 30/(1/5) = 30*(5)

 

[crunchberries]

Not quite true (as you can see, if you substitute x=150).


The following are correct equations.

0.2x = 30

(20/100)x = 30

30 divided by 0.2 (aka 20/100 aka 1/5) is 150

:cool:

Also, do you know? Dividing by a ratio is the same as multiplying by its reciprocal.

In other words:

0.2x = 30

(1/5)x = 30

x = 30/(1/5) = 30*(5)

Ah, yeah. I understand now. Thanks for the help!