Question

HELP FOR MEDAL!!
@misty1212

In Honolulu, Hawaii, the forecast for the next three days is for high temperatures of 80°, 81°, and 80°.
1st objective:
What would the temperature on the fourth day need to be to have a 4-day average of °87?
2nd objective:
The perimeter of the Hawaiian island of Oahu is approximately 230 miles. If the island were a rectangle with a length that is 35 miles longer than its width, write a system of two-variable equations that you could use to find its length.
3rd objective:
Solve the system of equations using substitution or linear combination. Show

Answer 1

HI again!!

Answer 2

hi thanks for coming to help me!

Answer 3

no problem!

Answer 4

i guess it would have to be pretty hot to get a four day average of 87
we can solve it by calling it \(x\), taking the average\[\frac{80+81+80+x}{4}\] and setting it equal to \(87\) to see what we get

Answer 5

in other words, solve
\[\frac{80+81+80+x}{4}=87\] first add all that stuff

Answer 6

i get
\[\frac{241+x}{4}=87\] so multiply by \(4\) and get
\[284+x=348\]

Answer 7

subtract and you are done

Answer 8

is x 64 @misty1212?

Answer 9

i doubt it

Answer 10

what is \(348-241\)?

Answer 11

107?

Answer 12

oh i see i made a typo sorry

Answer 13

yeah seems hot doesn't it?
lets check the answer

Answer 14

compute
\[\frac{80+81+80+107}{4}\] and see if you get \(87\)

Answer 15

i do!

Answer 16

ready for number two?
The perimeter of the Hawaiian island of Oahu is approximately 230 miles. If the island were a rectangle with a length that is 35 miles longer than its width, write a system of two-variable equations that you could use to find its length.

Answer 17

yep how do I do that @misty1212?

Answer 18

it wants a system of two equations, so i guess we have to do that

Answer 19

the perimeter is \(2l+2w\) so one equation is
\[2l+2w=230\]

Answer 20

then since the length is 35 miles longer than the width, you have
\[l=w+35\]

Answer 21

ooops typo
the two equations are
\[2l+2w=230\\
l=w+35\]

Answer 22

you good with that?

Answer 23

yep, I see it makes sense @misty1212

Answer 24

ok so on to
3rd objective: Solve the system of equations using substitution or linear combination. Show

Answer 25

since we know \(l=w+35\) we can substitute it in to the top equation and turn '
\[2l+2w=230\] in to
\[2(w+35)+2w=230\] and solve for \(w\)

Answer 26

here are a few ways to solve this
i would start by dividing by 2 to get
\[w+35+w=115\] or
\[2w+35=115\] and solve that one

Answer 27

hmm w=35 too @misty1212?

Answer 28

oh no never mind it's 40

Answer 29

thanks again for the help @misty1212!