Question

Evan is making a table that will be created in the shape of the figure below. The table top is a triangle attached to a rectangle. To purchase the right amount of paint, he needs to know the area of the table top. He can only spend $10 on paint, which is enough to cover 150 ft2 of surface area. What is the maximum length of the base of the rectangle he can build?

Answer 1

i put it in wrong subject :p

Answer 2

one*

Answer 3

Why not?

Answer 4

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Answer 5

anyhow, the wording is a bit off, thus I had to check and recheck
it turns out that Evan, is going to build the table, he knows the Area of the triangular part, but he doesn't know the Area of the rectangular part

he can only use $10 for painting, after he's done that is, which will yield 150 square feet

so whatever the Area of the rectangular part is, must fit within that constraint

so the Area of the triangle, ADDED to the Area of the rectangle must be EQUALS OR LESS than 150

it can't be more than 150, because Evan is not allowed to spend for more than that for the paint when he's done

\(\bf \textit{area of a triangle } = \cfrac{1}{2} (base)(height) \implies \cfrac{1}{2} (4)(6)\\
\textit{area of a rectangle} = x \times 6\\
\textit{triangle + rectangle areas} = \left[\cfrac{1}{2} (4)(6)\right] + \left[x \times 6\right]\\
\textit{thus our inequality}\\
\left[\cfrac{1}{2} (4)(6)\right] + \left[x \times 6\right] \le 150 \implies \cfrac{24}{2}+6x \le 150 \implies 12 + 6x \le 150\)

I think you can get it from there :)

Answer 6

so i have to simplify?

Answer 7

So the answer is 132?

Answer 8

well, I didn't get 132 for "x", but yes, you have to simplify and solve for "x"

Answer 9

wouldn't u do
150-12
138-6?
and then u have x left
x=132?

Answer 10

ahemm. well, notice that 6 is MULTIPLIER, a factor, is not ADDING or SUBTRACTING in the inequality

Answer 11

so u would divide it not subtract!!!
so 138/6!!!

Answer 12

so the answer would be 23?

Answer 13

\(\bf 12 + 6x \le 150 \implies 6x \le 138 \implies \cfrac{6x}{6} \le \cfrac{138}{6}\)


yes, \(\bf x \le 23 \) :)

Answer 14

yay ty can u help me with 2 more?

Answer 15

they should not take that long

Answer 16

if I have the time, sure, post anew so we can all see it and help and revise each other :)

Answer 17

Im actually in the test right now ...

Answer 18

here is the question...

As the number of pages in a photo book increases, the price of the book also increases. There is an additional shipping charge of 15%. The price of a book can be modeled by the equation below where, P = the price of the book, 20 is the printing charge, 0.5 is the charge per page, and x = the number of pages.

P = (20 + 0.5x) + 0.15(20 + 0.5x)

Jennifer wants to purchase a book but only has $62.10 to spend. What is the maximum number of pages she can have in her book?

i got 273.33

Answer 19

hmm.. a bit too much

Answer 20

sorry

Answer 21

116.16?

Answer 22

\(\bf P = (20 + 0.5x) + 0.15(20 + 0.5x)\\
\textit{she would like to only spend }\$62.10\\
P = 62.10\\ \quad \\
62.10 = (20 + 0.5x) + 0.15(20 + 0.5x)\\ \quad \\ \implies 62.10 = 20+0.5x + 0.15(20) + 0.15(0.5x)\)

Answer 23

23.65?

Answer 24

Hi joe im running out of time on my test...i have like 3 minutes left...

Answer 25

well, just add and divide terms

Answer 26

20.87?

Answer 27

she got more pages than that

as far as helping with tests, well, you're supposed to cover all this before that, we can help you if you don't understand something, but the tests are there for you to do them

Answer 28

thanks for ur help doe i will try to relearn the formula!

Answer 29

yw

Answer 30

one more woule it be 41.23

Answer 31

I don't know