# A few basic problems.

#### Sky_J

##### New member
Hi, I'm studying for a test coming up and was wondering if someone could help me refresh my memory on how to do few basic problems. It's been a very long time since I've done stuff like this, so can someone help?

1.) Alfred wants to invest $4,000 at 6% simple interest rate for 5 years. How much interest will he receive? 2.) The city council has decided to add a 0.3% tax on motel and hotel rooms. If a traveler spends the night in a motel room that costs$55 before taxes, how much will the city receive in taxes from him?

3.) Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?

4.) The sales price of a car is $12,590, which is 20% off the original price. What is the original price? I know that these are simple, but like I said, I haven't done stuff like this in a while and can't remember how to do them. Thanks for any and all help, Sky J. #### stapel ##### Super Moderator Staff member In general, to find the percentage of something, multiply. For instance: __twelve percent of 47: (0.12)(47) = 5.64 Sky_J said: 1.) Alfred wants to invest$4,000 at 6% simple interest rate for 5 years. How much interest will he receive?
The simple-interest formula (which you will need to memorize) is "I = Prt", where "I" is the amount of interest earned, "P" is the principal, "r" is the interest rate (as a decimal), and "t" is the number of years.

Plug the given values into the formula, and simplify to find the answer.

Sky_J said:
2.) The city council has decided to add a 0.3% tax on motel and hotel rooms. If a traveler spends the night in a motel room that costs $55 before taxes, how much will the city receive in taxes from him? Find point-three percent of fifty-five. Sky_J said: 3.) Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? This isn't mathematical, so much as logical. What would happen if, against all expectation, she started pulling out only red beans? Sky_J said: 4.) The sales price of a car is$12,590, which is 20% off the original price. What is the original price?
If the sale price is twenty percent, or 4/5, of the original price, then the original price is 5/4 of the sale price. Recalling that "of" means "times" in this context, find the original price.

Eliz.

#### tkhunny

##### Moderator
Staff member
Since you state that it has been a while AND you think they should be simple, I'll just throw them at you and see if we ring any bells. Feel free to ask for better details.

Sky_J said:
1.) Alfred wants to invest $4,000 at 6% simple interest rate for 5 years. How much interest will he receive? SimpleInterest = Principal * Rate * Time SimpleInterest = ($4000)*(.06)*(5) = ??

2.) The city council has decided to add a 0.3% tax on motel and hotel rooms. If a traveler spends the night in a motel room that costs $55 before taxes, how much will the city receive in taxes from him?p Tax = Basis*Rate Tax = ($55)*(0.3%) = ($55)*(0.003) = ?? 3.) Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? That's a funny question. The jelly beans are in her hand or in her pocket. She needs to remove none from her pocket to ensure at least one of each color. If you mean in her HAND ONLY, then 9. It's just a think problem. Let's see you do it in 8 or fewer. 4.) The sales price of a car is$12,590, which is 20% off the original price. What is the original price?
Discount = OriginalPrice * Percentage
SalePrice = OriginalPrice - Discount = OriginalPrice - (OriginalPrice * Percentage) = OriginalPrice*(1-Percentage)
12590 = OriginalPrice*(1-0.20)
OrigianlPrice = 12590/(1-0.2) = ??[/quote]

#### Sky_J

##### New member
Thanks so much for the help. I understood all but tkhunny's explaination of #4. I'm really bad at getting information out of word problems, and that's pretty much all that will be on the test. Stuff like this really confuses me:

If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

It doesn't make sense...

#### Denis

##### Senior Member
Sky_J said:
[Thanks so much for the help. I understood all but tkhunny's explaination of #4.]

What's wrong with tk's explanation?!

x = original car price
So x minus 20% of x = 12950 ; ok?
same as: x - .2x = 12950 ; ok?
There's a 1 in front of that 1st x: 1x - .2x = .8x ; get it?
SO: .8x = 12950
x = 12950 / .8 = 16,187.50, which is car's original price...
GOOD NEWS: them discount things ALL work that EASY way!

[I'm really bad at getting information out of word problems, and that's pretty much all that will be on the test. Stuff like this really confuses me:
If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?
It doesn't make sense...]

Per minute performances:
Steven: 20/5 = 4
Sue: 20/10 = 2
Jack: 20/15 = 1 1/3

So, in 1 minute, 4 + 2 + 1 1/3 = 7 1/3 of the 20 drinks are mixed;
in 2 minutes, 14 2/3 of the 20 drinks are mixed...
ok? Can you finish it?

#### Sky_J

##### New member
awesome. Ok, so the answer to that last one there would be somewhere around 2 min. 45 sec.

And the way you explained the percentage thing made more sense, but what if you have more than one? like this one:
An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for \$306. How much did it originally cost?

Could you just show me how it sets up? because that's the part I don't understand...

Thanks for all the help from everyone!
-Sky J.

#### Gene

##### Senior Member
Same thing. You get a new price after the first discount. You get the second discount on that price. Or that comes out to
p(1-d<sub>1</sub>)(1-d<sub>2</sub>) = the final price.

BTW, TKH fell asleep on the jelly beans. It is 13. Think about what Stapel said about bad luck. Apply it to red and green beans.

#### Sky_J

##### New member
Gene said:
Same thing. You get a new price after the first discount. You get the second discount on that price. Or that comes out to
p(1-d<sub>1</sub>)(1-d<sub>2</sub>) = the final price.

BTW, TKH fell asleep on the jelly beans. It is 13. Think about what Stapel said about bad luck. Apply it to red and green beans.
Alright, I'm really sorry about this, but I'm not seeing what you mean with that formula up there where p(1-d<sub>1</sub>)(1-d<sub>2</sub>) = the final price. What numbers do you plug in? Sorry for the cluelessness...

#### Gene

##### Senior Member
Sorry, I used p for the price instead of x.
306 = x*(1-.1)(1-.15) =
x*.9*.85
x = 306/(.9*.85)
Or you could do it in two steps.
u = 306/.85 and
x = u/.9
It works out the same

#### tkhunny

##### Moderator
Staff member
Gene said:
BTW, TKH fell asleep on the jelly beans. It is 13. Think about what Stapel said about bad luck. Apply it to red and green beans.
I still think the answer is zero (0). In the absence of zero (0), however, let's go with 13.