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Alex Ar [27]
1 year ago
8

Josie sold 790 tickets to a local car show for a total of $4,390.00. A ticket for a Child costs $4.00 and adult ticket costs $7.

00. How many of each ticket did she sell? A) Children’s ticket? B) Adult Ticket?
Mathematics
1 answer:
Papessa [141]1 year ago
3 0

Let's define the following variables first.

A = number of tickets sold for adults

C = number of tickets sold for children

From the question, we can say that or form the following equations:

1. A + C = 790 tickets

2. $7A + $4C = $4, 390

The first equation can also be written as A = 790 - C. We can use this equation and replace "A" in the second equation.

7(790-C)+4c=4,390

From that, we can solve "C" by solving the equation formed above.

\begin{gathered} \text{Distribute 7 to the terms inside the parenthesis.} \\ 7(790)-7(C)+4C=4,390 \\ 5,530-7C+4C=4,390 \\ \text{Subtract 5,530 on both sides of the equation.} \\ -7C+4C=-1140 \\ -3C=-1140 \\ \text{Divide -3 on both sides.} \\ C=380 \end{gathered}

Therefore, 380 tickets for children were sold.

Since there are 790 tickets in total that are sold and 380 tickets for children were sold, we can say that 410 tickets for adult was sold.

\begin{gathered} A=790-C \\ A=790-380 \\ A=410 \end{gathered}

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the perimeter of a pool table is 30 ft.The table is twice as long as it is wide.what is the length of the pool table.
noname [10]
Perimeter is legnth +legnth + width + width or
P=2L+2W

L=2W
subsitute L=2W for L in P=2L+2W

P=2(2W)+2W
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we know that Perimiter=30 so
30=6W
divide both sides by 6
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L=2(5)
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to check
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checks


Legnght=10
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3 years ago
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solmaris [256]
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The mass, m grams, of a radioactive substance, present at time t days after first being observed, is given by the formula m=24e^
Reika [66]

Answer:

(i) The value of<em> m</em> when t = 30 is 13.2

(ii) The value of <em>t</em> when the mass is half of its value at t=0 is 34.7

(iii) The rate of the mass when t=50 is -0.18            

Step-by-step explanation:

(i) The <em>m</em> value when t = 30 is:

m = 24e^{-0.02t} = 24e^{-0.02*30} = 13.2

Then, the value of<em> m</em> when t = 30 is 13.2

(ii) The value of the mass when t=0 is:

m_{0} = 24e^{-0.02t} = 24e^{-0.02*0} = 24    

Now, the value of <em>t </em>is:

ln(\frac{m_{0}/2}{24}) = -0.02t

t = -\frac{ln(\frac{24}{2*24})}{0.02} = 34.7

Hence, the value of <em>t</em> when the mass is half of its value at t=0 is 34.7

(iii) Finally, the rate at which the mass is decreasing when t=50 is:

\frac{dm}{dt} = \frac{d}{dt}(24e^{-0.02t}) = 24(e^{-0.02t})*(-0.02) = -0.48*                            (e^{-0.02*50}) = -0.18

Therefore, the rate of the mass when t=50 is -0.18.

I hope it helps you!                  

3 0
2 years ago
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