POW #13 Say ¨cheese¨

Question

Mr. peabody has to take a taxi home from the cheese shop. the fare is $0.90 for the first 1/2 km and $0.12 for each additional 1/8 km how far is his home for the shop if he spends $2.80? How much would his taxi cost for a 2 km trip? A 4km trip, A 6km trip or a 8km is there a pattern to help figure out the pattern. describe any patterns you see as a result of your calculations

Answer 1

Hello this is Justin from the Chicagoland area, IL :)

 

For the first question, what you don't know is "how far is his home" so create a variable to represent this. Keep in mind that since he spent more than 90 cents we know he lives at least 1/2km away from the shop, so our variable really represents "how much further than the 1/2km does he live from the shop." Let's just use x cuz that's what the cool math people like me would use, but you can use any symbol or letter you want. :)

 

So our equation would look like this: $.90 + $.12x = $2.80. They also threw in another sneaky thing that the 12 cents is for each 1/8km. So once we find what x is, that's how many 1/8km increments he lives from the shop. We'll worry about that later let's just solve for x right now.  Subtract the .90 from both sides to get $.12x = $1.90.  Now divide both sides by .12 to get x by itself. We get x = 15.83333. So this means Mr. Peabody lives 15.83333 increments of 1/8km away from the shop. To get the exact distance, multiply 15.83333 (which is 15 and 5/6) by 1/8 and then add the 1/2km to that, and you'll get your answer. :)

 

To get the rest of your answers, just use the same equation $.90 + $.12x = y where y is your total depending on your trip distance. Again since the first .90 is for the first 1/2km, you need to subtract that from what the problem is asking you first. Then take your new total and plug it in for x each time, but again don't forget to multiply it by 1/8 because the $.12 is for EACH 1/8km. So for the first one, a 2km trip would cost $.90 + $.12(12) = $2.34 because after taking away the 1/2km from the 2km, you are left with 1 and 1/2km, which is 12 increments of 1/8km. Think of the 1 and 1/2 as 8/8 and 4/8km. so you have 8 1/8 increments for the 1km, and 4 1/8 increments for the last 1/2km (4/8 = 1/2). 

 

I hope that wasn't confusing! So for a 4km trip, you have 3 and 1/2km left over after the initial $.90 charge for the first 1/2km. So you have 28 increments of 1/8 (8/8 for each 1km, and then 4/8 for the last half km). So plug in 28 for x into the same equation. 

Let me know if you have any further questions! Have a good one!

 

-Justin