Nick works two jobs to pay for college. He tutors for $15 per hour and also works as a bag boy for $8 per hour. Due to his class and study schedule, Nick is only able to work up to 20 hours per week but must earn at least $150 per week. If t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy, which system of inequalities represents this scenario?

Question

happyfeet8040 · Answer

t + b greater than or equal to 20
15t + 8b = 150

 t + b less than or greater to 20
15t + 8b greater than or equal to 150

 t + b less than or greater to 20
15t + 8b less than or greater to 150

 None of the systems shown represent this scenario.

happyfeet8040 · Answer

Someone please help! I will give a medal.

imstuck · Answer

Ok what you have to do here is relate the hours of tutoring plus the hours of bagging to the hours he is allowed to work, which is 20.  Then you relate what he makes tutoring plus what he makes bagging to what he must earn which is 150.  So the first equation relating the hours is this:
$$t+b \le20$$What this says is that the hours of tutoring plus the hours of bagging has to be less than or equal to 20 hours.

imstuck · Answer

The other inequality relating the money earned and needed is this:$$15t+8b \ge 150$$This says that the 15 dollars per hour for tutoring plus the 8 dollars per hour for bagging must be at least 150 dollars.  So that is your second inequality.

imstuck · Answer

So the solution should read (and I think you may have some typos in your choices):
t + b is less than or equal to 20
                     and
15t+8b is greater than or equal to 150

imstuck · Answer

I think it's the second choice with a typo made on accident.

imstuck · Answer

If not, it is "none of the systems..."  But I think it is supposed to be the second one.

happyfeet8040 · Answer

I agree! It makes more sense now, thank you so much. :)

happyfeet8040 · Answer

Can you help me with a couple more.

happyfeet8040 · Answer

@IMStuck

imstuck · Answer

Sure.  What do you have?

happyfeet8040 · Answer

Sophia invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of her investment after x years:

f(x) = 500(1.05)x

What was the average rate of change of the value of Sophia's investment from the second year to the fourth year?

 14.13 dollars per year

 28.25 dollars per year

 50.00 dollars per year

 56.50 dollars per year

imstuck · Answer

Is that $$f(x)=500(1.05)^{x}$$or$$f(x)=500(1.05)x$$

imstuck · Answer

Important.  They are very different from each other.

happyfeet8040 · Answer

How are they different? Sorry, I'm trying to understand.. I'm not so great at math haha.

imstuck · Answer

it's the first one.

imstuck · Answer

Is it the first one?  That is x as an exponent.

imstuck · Answer

I'm going with that one.

imstuck · Answer

The general formula is this:$$A=A _{0}(1+r)^{t}$$

imstuck · Answer

Going with that one and using the formula and x = 2, you have this$$A=500(1.05)^{2}$$and A = 551.25

imstuck · Answer

Now we will do it with 4 years:$$A=500(1.05)^{4}$$and A = 607.75

imstuck · Answer

Now subtract the first from the second, the lower from the higher, and the difference is 56.50  Do you see that answer in your choices?

imstuck · Answer

Are you there?  I'm here to help if you need more...

happyfeet8040 · Answer

Yes, I'm here. Sorry, I was doing something.

happyfeet8040 · Answer

So, you think it's the first one? @IMStuck