A local department store is going out of business and is selling every item for 40% off the original price. The discount will be taken at the register. Gene buys 2 pairs of shorts for $18.77 each, one polo shirt for $21.87, and a pair of shoes for $34.24. Gene wants to know approximately how much he will pay. A) use your own words to describe the big-picture ideas in the scenario. B) use your own words to list out each important detail in the scenario. C) Estimate (round first) what Gene will pay for the items after the discount is taken.

Gene would pay approximately $56.19 for his total purchase of two pairs of shorts, one polo shirt, and one pair of shoes.

Step-by-step explanation:

First identify what you know:

1) Every item in the store is 40% off the ticketed price (original price)

2) Gene buys two pairs of shorts for $18.77 each.

3) Gene buys one polo shirt for $21.87.

4) Gene buys one pair of shoes for $34.24.

5) Discount is taken at the register.

So, assuming that each price given, IS the original price, we need to figure out exactly how much Gene paid with the 40% discount. We can solve this in two different ways.

1) Individually calculate 40% of each price of each item, and then add them up to find the total discounted price of all the items.

2) Add all the original items and calculate 40% off the original price, and subtract that amount from the original price.

I find it simplest to add up the original prices, and find the total, and then calculate the discounted (40%) total.

Original total = (2 x $18.77) + ($21.87) + ($34.24)

Original Price = ($37.54) + ($21.87) + ($34.24)

Original Total Price: $93.65

Now, we know that without the discount, the total for ALL the items would be $93.65. Now, we just need to find out what 40% of 93.65 is! TO do this, simply multiply 93.65 by 40% OR multiply 93.65 by 0.40.

93.65 x 0.40 = 37.46

So, 40% of $93.65 is $37.46. Now we just need to subtract that percentage to find the discounted price!

$93.65 - $37.46 = $56.19

Gene paid approximately $56.19 for two pairs of short, one polo shirt, and one pair of shoes, at a discount of 40% off.

Hope this helps! :)

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: