Question

please help with 2 math questions! Will give medal!!

Answer 1

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 2

also The sum of three consecutive integers is 267. What is the largest integer?

Answer 3

@Easyaspi314 can you help with this?

Answer 4

Yes.

Answer 5

For the second question I got 91 but it wasn't right so I am not sure how to do it

Answer 6

3 consecutive integers are 3 integers, one after each other.

Let x = first integer
x + 1 = second integer
x+ 3 = third integer

Since the sum is 267, your equation is:

x + (x + 1) + (x + 2) = 267

Answer 7

or, 3x + 3 = 267
3x = 264
x = 88

Answer 8

So the LARGEST integer is x + 2, so 88 + 2 = 90

90 is the largest integer.

Answer 9

Makes sense?

Answer 10

oh okay I see

Answer 11

In the beginning, I wrote x+3 is the 3rd integer, it should say x+2 is the 3rd integer. But the equation and solution and final answer is all correct.

Answer 12

So how about the first one I dont get how to do it

Answer 13

Any other question?

Answer 14

Yes I have the first question still @Easyaspi314

Answer 15

I got to 1/2(4)(6) + (X times 6)

Answer 16

For the tabletop...it is made up of a triangle and rectangle.

Area of the triangle is (1/2)(base)(height) = (1/2)(4)(6) = 12
Area of the rectangle is (length)(width) = 6(x) = 6x

Total area of the table top is 12 + 6x.

Agree?

Answer 17

yes thats where i got to

Answer 18

So would it be possible to find x?

Answer 19

But the area of the tabletop cannot exceed 150 (square feet).

Therefore, 12 + 6x < or = 150.
Solving that inequality, we get

6x < 138

x < or equal to 23

That means x can be at most 23 feet.

Answer 20

Makes sense?

Answer 21

oh okay thank you

Answer 22

And, we can check and show, that x = 23 is the maximum.

Answer 23

Whats the total area of the tabletop when x = 23?

Answer 24

Well, the triangle will have area of 12, as we said before, and the rectangle will have area 6(23) = 138

so 12 + 138 = 150

Therefore, x = 23 is the maximum that the length of the rectangle can be.

Answer 25

Thank you!

Answer 26

Welcome. And, by the way, the idea of $10 on paint that is given in the problem doesnt play a role in solving the proble. Even if the paint is a million dollars, x = 23 is the maximum length the rectangle will be if the area is to be no more than 150 sq ft.