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Naddika [18.5K]
3 years ago
11

The number of walls, w, that Joe can paint in t hours is given by the equation w=32t−1. Answer the questions below.

Mathematics
1 answer:
klio [65]3 years ago
3 0

We have been given an equation w=\frac{3}{2}t-1 that represents umber of walls, w, that Joe can paint in t hours. We are asked to find the number of hours it will take Joe yo paint 7 walls.

To solve our given problem, we will substitute w=7 in our given equation as:

7=\frac{3}{2}t-1

Let us solve for t.

7+1=\frac{3}{2}t-1+1

8=\frac{3}{2}t

8\cdot\frac{2}{3}=\frac{2}{3}\cdot\frac{3}{2}t

\frac{8\cdot2}{3}=t

\frac{16}{3}=t

Therefore, it will take \frac{16}{3} hours Joe to paint 7 walls.

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2 years ago
The junior and senior students at Mathville High School are going to present an exciting musical entitled, "Math, What is it Goo
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Some parts are missing in the queston. Find attached the picture with the complete question

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                   \large\boxed{\large\boxed{161}}

Explanation:

Let's put the information in a table step-by step.

                                                (number of remaining students)

                                                        Juniors          Seniors

Condition

  • Initially                                           J                     S
  • 15 seniors left                                                   S - 15
  • Twice juniors as seniors         2(S - 15)
  • 3/4 of the juniors left              1/4×2(S - 15)
  • 1/3 of seniors left                                             2/3×(S - 15)

At the end, there were 8 more seniors than juniors:

  • 2/3×(S - 15) -  1/4×2(S - 15) = 8

Now you have obtained one equation, which you can solve to find S, the number of senior students, and then the number of junior students.

Solve the equation:

2/3\times (S - 15) -  1/4\times 2(S - 15) = 8

  • Mutilply all by 12:

8(S - 15)-6(S - 15)=96

  • Distribution property:

8S-120-6S-90=96

  • Addtion property of equalities:

8S-6S=96+120+90

  • Add like terms:

2S=306

  • Division property of equalities:

S=306/2=153

That is the number of senior students that came out to the information meeting, but the number of students remaining to perform in the school musical is (from the table above):

2/3\times (S-15)+1/4\times 2(S-15)

Just substitute S with 153 fo find the number of students that remained to perfom in the musical:

          2/3\times (153-15)+1/4\times 2(153-15)\\ \\ 2/3(138)+1/2(138)

          161

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