Question

Jasmin traveled a certain distance at exactly 35 mph and then she traveled another distance at exactly 55 mph. Write an equation in standard form that models this situation if Jasmin went a total distance of 620 miles.

Answer 1

amishjeb, the formula is

d = r*t

not

t = r*d

Answer 2

True.

Answer 3

if you let

x = time spent going 35 mph
y = time spent going 55 mph

note: both times are in hours

then

35x is the distance you go 35 mph for x hours
55y is the distance you go 55 mph for y hours

Answer 4

@jim_thompson5910 so it would look like 620=35+55t?

Answer 5

add the two distances to get 35x+55y

the total distance traveled is 35x+55y and this is for x+y hours

Answer 6

we're told the total distance is 620 miles, so this means

35x+55y = 620

Answer 7

Jim, I had something else come up like this. Maybe you could help me.
Can you only use one variable and set it up like this:
35x +55(620-x)=620?

Answer 8

you could rewrite it, but that's effectively what they want

Answer 9

no because x+y is the total TIME, not distance

Answer 10

you cannot say x+y = 620 and then rewrite it to get y = 620 - x

Answer 11

if you knew that it took 10 hours, then you could say x+y = 10 ---> y = 10 - x

but we don't have that kind of info

Answer 12

Ahhhh alright. Thanks. I'll try not to post bad info next time :) Sorry guys.

Answer 13

that's ok, it's all part of the learning process

Answer 14

don't be afraid to get it wrong

Answer 15

so basically you sub. in ax+by=c for a=35 and b=55 and c= 620 all together

Answer 16

yes using the steps I showed above and you could reduce things, but 35x+55y = 620 is an equation in standard form, so you can stop there

Answer 17

you could keep going and divide everything by 5 to get

35x/5 = 7x
55y/5 = 11y
620/5 = 124


so

35x+55y = 620

turns into

7x + 11y = 124


but this step is optional really

Answer 18

y would you divide everything by 5 im confused

Answer 19

5 is the GCF of the numbers 35, 55, 620

Answer 20

you could divide everything by the GCF so it fully reduces (and everything will stay a whole number)

Answer 21

oh ohk so you could do the same for You are going shopping for some new school clothes. You see some shirts and jeans that you like. The shirts are $35.99 each and the jeans are $65.00 each. You have $350 to spend.

Answer 22

so it would be 35.99x+65y=350 and then the gcf =5 ? right

Answer 23

in this case, the GCF wouldn't apply because 35.99 isn't a whole number

Answer 24

what you could do though is multiply everything by 100 to make 35.99 turn into 3599 (a whole number)


35.99x*100 = 3599x
65y*100 = 6500y
350*100 = 35000


so the equation

35.99x+65y=350

becomes

3599x+6500y = 35000


which is now in standard form

Answer 25

why would you multiply by 100

Answer 26

because standard form is Ax+By = C

where A,B,C are whole numbers (A is usually nonnegative)

Answer 27

but why 100 though

Answer 28

well to move the decimal point 2 spots to the right, you multiply by 100

Answer 29

if we had 3.599 and we wanted to move the decimal 3 spots to the right, we'd multiply it by 1000

Answer 30

oh ok thank you for breaking it down it really makes alot of sense now

Answer 31

I'm glad it's all clicking, you're welcome

Answer 32

:)

Answer 33

@jim_thompson5910 i have one more question