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notsponge [240]
3 years ago
12

If 112 people attend a concert and tickets for adults cost $2.25 while tickets for children cost $and total receipts for the con

cert was $231.00, how many of each went to the concert?
Mathematics
2 answers:
MA_775_DIABLO [31]3 years ago
5 0

Answer:

70 adults

42 children

Step-by-step explanation:

A + C = 112

A = 112 - C

2.25A + 1.75C = 231

2.25(112 - C) + 1.75C = 231

252 - 2.25C + 1.75C = 231

21 = 0.5C

C = 42

A = 112 - C

A = 112 - 42

A = 70

Brut [27]3 years ago
4 0

Answer:

42 child and 70 adult

Step-by-step explanation:

Let a = number of adult tickets

c = number of child tickets

a+c = 112

2.25a + 1.75c = 231

Solve the first equation for a

a = 112-c

Substitute this into the second equation

2.25(112-c) + 1.75c = 231

Distribute

252 - 2.25c +1.75c = 231

Combine like terms

252 -.5c = 231

Subtract 252 from each side

252-252 -.5c = 231-252

-.5c = -21

Divide each side by -.5

-.5c/-.5 = -21/ -.5

c = 42

Now can find a

a = 112-c

a = 112-42

a = 70

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In an arithmetic​ sequence, the nth term an is given by the formula an=a1+(n−1)d​, where a1 is the first term and d is the commo
Dmitry_Shevchenko [17]

Answer:

a_{10} = \frac{10}{65536}

Step-by-step explanation:

The first step to solving this problem is verifying if this sequence is an arithmetic sequence or a geometric sequence.

This sequence is arithmetic if:

a_{3} - a_{2} = a_{2} - a_{1}

We have that:

a_{3} = 40, a_{2} = 10, a_{3} = \frac{5}{2}

a_{3} - a_{2} = a_{2} - a_{1}

\frac{5}{2} - 10 = 10 - 40

\frac{-15}{2} \neq -30

This is not an arithmetic sequence.

This sequence is geometric if:

\frac{a_{3}}{a_{2}} = \frac{a_{2}}{a_{1}}

\frac{\frac{5}[2}}{10} = \frac{10}{40}

\frac{5}{20} = \frac{1}{4}

\frac{1}{4} = \frac{1}{4}

This is a geometric sequence, in which:

The first term is 40, so a_{1} = 40

The common ratio is \frac{1}{4}, so r = \frac{1}{4}.

We have that:

a_{n} = a_{1}*r^{n-1}

The 10th term is a_{10}. So:

a_{10} = a_{1}*r^{9}

a_{10} = 40*(\frac{1}{4})^{9}

a_{10} = \frac{40}{262144}

Simplifying by 4, we have:

a_{10} = \frac{10}{65536}

3 0
4 years ago
A triangle has a perimeter of 91 centimeters. Each of the two longer sides of the triangle is three times as long as the shortes
Mkey [24]

9514 1404 393

Answer:

  13 cm, 39 cm, 39 cm

Step-by-step explanation:

If x is the short side, then the other two sides are 3x and 3x. The perimeter is the sum of side lengths:

  x +3x +3x = 91

  x = 91/7 = 13

  3x = 3(13) = 39

The length of the short side is 13 cm; the other two sides are 39 cm.

4 0
2 years ago
If S is the midpoint of RT , RS=8x+11 and ST =14x-1 find x
garri49 [273]

Answer:

From the given, we establish this relationship:

RS + ST = RT

RS = ST since S is the midpoint of RT

Thus, let's use RS = ST to find x,

By substituting the given expressions:

RS = ST

8x + 11 = 14x - 1

12 = 6x

x = 12/6

thus,

x = 2

4 0
3 years ago
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