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4 years ago

How do you do this problem?

Mathematics

1 answer:

scoray [572]4 years ago

6 0

Answer:

An adult ticket costs $4. A child ticket costs $7.

Step-by-step explanation:

We want to find out the price of an adult ticket and the price of a child ticket. The unknowns in this problem are those two prices. Since they are unknown, we will choose a variable to represent each unknown.

Let a = price of one adult ticket

Let c = price of one child ticket

3 adult tickets and 9 child tickets sold for $75.

3 adult tickets cost 3a. 9 child tickets cost 9c. Together they cost 3a + 9c. They cost $75, so our first equation is

3a + 9c = 75

8 adult tickets and 5 child tickets sold for $67.

8 adult tickets cost 8a. 5 child tickets cost 5c. Together they cost 8a + 5c. They cost $67, so our second equation is

8a + 5c = 67

We have a system, of equations:

3a + 9c = 75

8a + 5c = 67

We will use the addition method and cancel out a. Multiply the first equation by -8. Multiply the second equation by 3.

-24a - 72c = -600

24a + 15c = 201

Add the two equations just above.

-57c = -399

c = 7

Now substitute c = 7 in the first original equation and solve for a.

3a + 9c = 75

3a + 9(7) = 75

3a + 63 = 75

3a = 12

a = 4

An adult ticket costs $4. A child ticket costs $7.

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4 years ago

Read 2 more answers

A designer is creating various open-top boxes by cutting four equally-sized squares from the corners of a standard sheet of 8.5

Oxana [17]

Answer:

L(x) = 11 - 2x

W(x) = 8.5 - 2x

V(x) = 4x³ - 39x² + 93.5x

Step-by-step explanation:

If a square of x sides length is cut from each corner of the sheet, then it meas the length and width of the box a shortened by x inces from each side, giving a total subtraction of 2 times x inches.

FORMULA FOR LENGTH:

Since, Length is the bigger side of the box. Therefore, it will be taken on 11 inches side of the paper:

L(x) = 11 - 2x

FORMULA FOR WIDTH:

Since, width is the smaller side of the box. Therefore, it will be taken on 8.5 inches side of the paper:

W(x) = 8.5 - 2x

FORMULA FOR VOLUME:

Volume is the product of length, width and time:

V(x) = L(x)*W(x)*H(x)

Height must be equal to the side folds which are equal to length of the side of square = x:

H(x) = x

Therefore,

V(x) = (11 - 2x)(8.5 - 2x)(x)

V(x) = (93.5 -22x -17x + 4x²)(x)

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