Secondary III • 9mo.
I'm not sure how to figure this question out
I'm not sure how to figure this question out
Explanation verified by Alloprof
This Explanation was verified by a member of the Alloprof team.
Hey FairSky4367!
I'm going to try to answer your question the best I can, since english isn't my first language and I learned maths in french.
Fist of all, you're going to have to find the rule, which is y = ax+b. You already have the b, since you know that his salary starts at 260$, even if he sells no shoes. So b is 260. Now to find a, you do y2-y1 divided by x2-x1, like you already wrote. You do it using the data they gave you in the table of contents. So this will give you 1,5. Your rule is:
y = 1,5x+260. Now, you have to find the second one to be able to compare.
You're going to do the same steps as the first one to find y = ax+b. To find a, repeat the formula you used before (y2-y1 divided by x2-x1) with the information his friend gave him. The result is approximately 1,86. So 1,86 is a. Now for b. You know the rule is y = 1,86x+b, and want to find b. So you're going to have to use one of the points his friend gave him. Either the 20 shoes sold for 280$, or the 300 pairs for 500$. I'm going to use the first one. So now, you have 280=1,86(20)+b. Now, all you have to do is use pemdas by multiplying. You'll get 280=37,2+b . In order to find b, you want to isolate it by moving the 37,2 to the other side. So you're going to subtract 37,2 from both sides, which leaves you with 242,8=b. Now you know the second rule is y=1,86x+242,8!
You're still not done though! You need to figure out which one is better for Carlos by replacing the x in these rules with 40 and 56. If he sells 40 shoes, the first store is better for him. However, if he sells 56 pairs or more, the second store would be the better option. Now, the answer for this problem isn't precise, because we don't know how much shoes Carlos is going to continue selling. However, we can see that he went down from last week. In that case, the first store is better for him. If he plans on selling more though, the seconde store would be more advantageous for him.
I hope I cleared everything for you and if I made a mistake, please let me know!