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Word problem: Before I was old enough to drive, my brothers had to take turns driving me around. In exchange for this, my mom told them that she would pay for their car insurance. The base insurance rate was $2500 minus $50 for every year the driver is insured with the company. My oldest brother, Jeff, had earned a good driver discount of $500 off. However, he also drove a sports car, which added $250 to his premium. Greg had not been driving long enough to earn a discount, but he drove a little pick-up so there was no additional cost. The cost of their insurance premiums can be described using the functions below: Jeff's insurance: J(x) = 2500 - 50x - 500 + 250 Greg's insurance: G(x) = 2500 - 50x where x is the amount of years the driver is insured with the company. 1. Find the function that models what my mom had to pay for both of them. 2. Find the cost of Jeff's insurance after four years with the company. 3. Find the cost of Greg's insurance after 2 years with the company.
There are more problems, but I thought I'd start off asking about these. I really, really don't just want the answer. I want to be able to work through this and really understand the concept, as I'll be taking a test, so please walk me through it and help me to solve it on my own. Thank you so much.
@ganeshie8 @Hero @iambatman
@TheSmartOne @Luigi0210 @Compassionate
So you have the equation for the amount both Jeff and Greg's insurance. 1. You need to find the TOTAL cost of the insurance that Jeff and Greg's mother is paying for. In example, let's say that my mom gave me 100 and my sister 250 dollars. How much money did our mother give us? How would you do this question? Thus, 100 + 250 = 300. Same concept here, but remember, you cannot add something like 20x + 20. You can only add like terms. Thus 20x + 20x = 40x. But 20x + 20 cannot be simplified further. 2. In the equation, x = years. So for question number two, it says that x = 4. You simply need to replace x with the number they gave you here. However, remember that 50x = 50 * x. Solve accordingly with the equations for Jeff's insurance: J(x) = 2500 - 50x - 500 + 250. 3. Same concept, x = years. How many years was Greg insured with the company? Then solve accordingly with the given function G(x) = 2500 - 50x
@jojokiw3 so in regards to #1, would I have to find like terms in order to find the total amount that their mom had to pay for them?
sorry if that sounded dumb, I'm just really trying to get a grasp on the concept here
You have to add the like terms together. :)
Give me a quick second. Try to do the question on your own. I'll be right back to see if it's right.
@jojokiw3 okay! thank you so much for your time by the way
@jojokiw3 would #1 look anything like f(x) = 5000-100x-500+250?
Well pretty much, but you can take it a bittt further. There's still some like terms. :)
@jojokiw3 you're right! so f(x) = 5000-100x-250?
One more haha!
@jojokiw3 I TOTALLY MISSED THAT - f(x)= 4750-100x?
Yep! Looks right to me!
@jojokiw3 thank you so much! okay, so let me look at question #2
Ok. Here's an example that may help explain the concept of a function. G(x) = 39x + 2x + 100. Then, If we make x = 2. Then, we get G(2) = 41(2) + 100, which equals 182.
@jojokiw3 so, would I set #2 up as j(x)=2500-50(4)-500+250?
@jojokiw3 so would the answer just be 2050?
@jojokiw3 so #3 would be 2400?
Yayaya! Yeah haha! I'll ask one more question to make sure you have it down. \[f(x) = 37x + 13x -200 +300. \] x = 10
So combine like terms first. Then plug x in and solve.
@jojokiw3 so 37(10)+13(10)+100 = 600
Haha there we go! Good job and good luck! :D
@jojokiw3 thank you!! can i open another thread with a few of the next problems under the same word problem and tag you?
@jojokiw3 4. In the 5th year, how much more did my mom have to pay for Greg than for Jeff? Use f(x)=2x-5 and g(x)=12-x^2 to evaluate the expression