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Dimas [21]
2 years ago
9

A group of seven adults went to the movies. The total cost of the movie tickets was $30. This doesn't seem possible, does it? Af

ter all, 30 is not evenly divisible by 7. Ah, but there's a hitch. The reason that $30 was the total cost was that some members of the group were senior citizens, so they got to see the movie at half price. How many of the group were senior citizens, and how much did the tickets cost?
Mathematics
1 answer:
Artyom0805 [142]2 years ago
4 0

Answer:

no. of senior citizens=x

no.of other people=7-x

cost=30=k(7-x)+(k/2)x. k is the cost of a ticket

k(7-x+x/2)

k(7-x/2)-30=0

k=60/(14-x)

now do trial and error substitution for (x<7) until u get a whole number for k also (k<30). if you have the skills you can suggest the number yourself

ie x= 2, k=5$

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Find the 13th term of the arithmetic sequence -3x – 1,42 + 4,112 + 9, ...
Strike441 [17]

Answer:

The 13th term is 81<em>x</em> + 59.

Step-by-step explanation:

We are given the arithmetic sequence:

\displaystle -3x -1, \, 4x +4, \, 11x  + 9 \dots

And we want to find the 13th term.

Recall that for an arithmetic sequence, each subsequent term only differ by a common difference <em>d</em>. In other words:

\displaystyle \underbrace{-3x - 1}_{x_1} + d = \underbrace{4x + 4} _ {x_2}

Find the common difference by subtracting the first term from the second:

d = (4x+4) - (-3x - 1)

Distribute:

d = (4x + 4) + (3x + 1)

Combine like terms. Hence:

d = 7x + 5

The common difference is (7<em>x</em> + 5).

To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:

\displaystyle x_n = a + d(n-1)

Where <em>a</em> is the initial term and <em>d</em> is the common difference.

The initial term is (-3<em>x</em> - 1) and the common difference is (7<em>x</em> + 5). Hence:

\displaystyle x_n = (-3x - 1) + (7x+5)(n-1)

To find the 13th term, let <em>n</em> = 13. Hence:

\displaystyle x_{13} = (-3x - 1) + (7x + 5)((13)-1)

Simplify:

\displaystyle \begin{aligned}x_{13} &= (-3x-1) + (7x+5)(12) \\ &= (-3x - 1) +(84x + 60) \\ &= 81x + 59 \end{aligned}

The 13th term is 81<em>x</em> + 59.

3 0
3 years ago
1. Andrew ran a marathon in about 1.56 x 10^4 s. (a) Write Andrews time in standard notation. (b) Evelyn ran a marathon in 4 h a
romanna [79]

Answer:

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  • (b)  Evelyn

Step-by-step explanation:

(a) 1.56×10^4 = 1.56×10000 = 15,600

(b) There are 3600 seconds in an hour, so Andrew's time was

  15600 s/(3600 s/h) = 13/3 h = 4 1/3 h

1/3 hour is 20 minutes, so Evelyn's time of 4:16 is shorter than Andrew's time of 4:20.

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Write a word problem that can be solved using the equation 2(h+8)=28
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Answer:

See below.

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2 times 8 more than the height of a garden wall is 28 feet. How high is the garden wall?

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6(2y-4)+p

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