Question

For the following problems show how the problem is set up, the work to solve the problem, along with the solution.

Jesse rents a moving van for $75 and must pay $2 per mile. The following week, Alex rents the same van, is charged $80 for the rental and $1.50 per mile. If they each paid the same amount and drove the same number of miles, how far did they each travel?

During a 4th of July weekend, 32 vehicles became trapped on the Sunshine Skyway Bridge while it was being repaved. A recent city ordinance decreed that only cars with 4 wheels and trucks with six wheels could be on the bridge

Answer 1

Try writing expressions for how much Jesse had to pay in total and for how much Alex had to pay in total. And then realize, because they both paid the same, that you can set those two expressions to be equal to each other

Answer 2

Idk what expressions to write! I have no clue how to do this stuff..

Answer 3

Start with the English language version... how much did Jesse have to pay total?

Answer 4

He paid $75, but he also paid $2 for every mile he drove. You don't know yet how far that is, but that's OK.

Jesse paid $75 + $2 times the number of miles, right?

Answer 5

In math, that is like 75 + 2(number of miles)... let's call "m" the number of miles.

so Jesse paid 75 + 2(m)

Answer 6

are you with me so far?

Answer 7

yes

Answer 8

sorry, stepped away.

So Alex paid $80 plus $1.50 per mile, or 80+1.50(m)

Ok

Answer 9

and Alex and Jesse paid the same, so 80+1.50(m) is equal to 75+2(m)

right?

Answer 10

So you can get all the numbers on one side and all the m terms on the other
80 + 1.50m = 75 + 2m
5 = 0.50m
m = 10 miles

Answer 11

Aaaaahhhhh , okay... Thanks :) Do you do the next one the same way?

Answer 12

yes, probably. you didn't paste the whole 2nd problem in... looks incomplete above, because it doesn't ask any questions

Answer 13

Oh sorry:
During a 4th of July weekend, 32 vehicles became trapped on the Sunshine Skyway Bridge while it was being repaved. A recent city ordinance decreed that only cars with 4 wheels and trucks with six wheels could be on the bridge at any given time. If there were 148 tires that needed to be replaced to due to damage, how many cars and trucks were involved in the incident?

Answer 14

yes, same approach. cars have 4 wheels each, trucks have 6, so the total number of tires equals some number of cars times 4 wheels each PLUS some number of trucks times 6 wheels each

Also, you know that the number of cars PLUS trucks equals 32, right?

Answer 15

wait... huh?

Answer 16

number of tires total is W (for "wheels")
# of cars is C
# of trucks is T
W = 4C + 6T = 148

Answer 17

Can you walk me through it again? I guess I rly didn't get it.. I am so confused! I'm sorry :/

Answer 18

I, like, half-way get it, I'm just not comprehending it very well.

Answer 19

Can you follow that last statement? It is totaling up all the tires that need repair... it's 4 for every car and 6 for every truck, and the problem tells you the total is 148. In fact, forget the W, you don't need it... just 4C + 6T = 148

Answer 20

are you with me on that part ? There's more, but that's the start.

Answer 21

Yes

Answer 22

good :)

The other thing you are given is that there were 32 vehicles total involved. So the number of cars PLUS trucks is 32, and you can write that in math as C + T = 32

Still with me? :)

Answer 23

yeah

Answer 24

So, now you need to figure out C and T

There is more than one way, but try this:

if C+T = 32, then T = 32 - C

Using T = 32 - C and the total wheels equation from a minute ago, 4C + 6T = 148
we can get T:

4C + 6T = 148
4C + 6(32-C) = 148 (sub in T = 32-C)
4C + 192-6C = 148
192-2C =148
192-148 = 2C
44 = 2C
C = 22

Answer 25

Then because T = 32 - C, if C is 22, T must be 32-22 = 10

so 22 cars and 10 trucks

Answer 26

whoah whoah whoah slow down, what?

Answer 27

:)

Answer 28

give me a minute to process, Lol

Answer 29

take your time, I just wanted to put it all up for you to see