Ask question

Ask question

All categories

4 years ago

13

A church luncheon made $842. Adult tickets cost $10 each and children's tickets cost $6 each. The number of children was 12 more

than twice the number of adults. How many of each ticket were sold?

1 answer:

Orlov [11]4 years ago

3 0

Solution: Let $x$ be the number of adult ticket's.

The number of child ticket $=2x+12$

We are given, that an adult ticket cost's $10 and child ticket costs $6. Also the church luncheon made $842.

Therefore,

$x \times 10 + (2x+12)6=842$

$10x+12x+72=842$

$22x=842-72$

$22x=770$

$x=\frac{770}{22}=35$

Therefore, the number of adult ticket's sold = 35

And the number of child ticket's sold = 2 x 35 + 12 = 70 + 12 = 82

You might be interested in

Find the unit vectors that are parallel to the tangent line to the parabola y = x2 at the point (2, 4).

skelet666 [1.2K]

Answer:

The unit vectors are:

$\vec u_1 = \left\\\vec u_2 = \left$

Step-by-step explanation:

Unit vectors that are a parallel to the tangent line have the same slope than the tangent line, thus we can find the slope of the tangent line, find directional vectors and then their corresponding unit vectors.

Finding the slope of the tangent line.

We can find the first derivative of the curve, which represents the slope of the tangent line of the curve at that point.

$y = x^2 \\ y'=2x$

At x = 2 we have

$y'= 2(2)\\y'= 4\\$

Thus we have slope m = 4, then the parallel unit vector has slope m = 4/1

Finding unit vectors.

From the slope m = 4/1, we can write it as a direction vector with x =1 and y = 4. Notice also that x = -1 and y = -4 would have given as as well slope m = 4 too.

$\vec u =$

Then in order to find the unit vector on that direction we can use the formula

$\hat u =\cfrac{\vec u}{|\vec u|}$

So finding the magnitude we get

$|\vec u |= \sqrt{(1)^2+(4)^2}\\|\vec u| = \sqrt{17}$

Then one unit vector that is parallel to the tangent line is

$\vec u_1 = \left$

And the second unit vector is

$\vec u_2 = \left$

The negative sign on both x and y components just tell us that we are aiming on the opposite direction as the first unit vector, yet both have the same value of the slope.

6 0

3 years ago

Two similar triangles are shown below:<br> Which two sets of angles are corresponding angles

Ksju [112]

Answer:

angle w and angle v; angle x and angle y (option 1)

Step-by-step explanation:

the little arc things are what tell you two angles are corresponding m

angles w and v both have two arc drawing things.

angle x and y have one

and the other angles that aren't labeled have three

3 0

3 years ago

(20a - 1) ÷ b when a= 2 and b= 13

mote1985 [20]

Answer:

3

Step-by-step explanation:

(20a - 1) ÷ b

a = 2

b = 13

(20(2) - 1) ÷ 13

(40-1)÷13

39÷ 13

= 3

3 0

4 years ago

Read 2 more answers

2. What is g(6)and what does it represent in the context of this example?

ahrayia [7]

Answer:

g(x) = 30

Step-by-step explanation:

Let the function representing line in graph 2 is,

g(x) = mx + b

Here m = slope of the line

b = y-intercept

Since the given line passes through origin (0, 0), y-intercept of the function will be 0.

Slope of the line = $\frac{\triangle y}{\triangle x}$

= $\frac{10}{2}$

= 5

Therefore, function will be g(x) = 5x

For x = 6,

g(6) = 30

This function represents that height of liquid in the cylinder is directly proportional to the amount of liquid poured in the cylinder.

3 0

4 years ago

Zoe keeps track of the miles per gallon her car gets per week. She has accumulated the following data: (1, 24), (2, 24.38), (3,

boyakko [2]

In order to find the <u>common difference</u> of the data in the problem you have to follow those steps

we know that

In an <u>Arithmetic Sequence</u> the difference between one term and the next is a constant. This constant is called <u>common difference</u>

Let

$x1=1\ y1=24$

$x2=2\ y2=24.38$

$x3=3\ y3=24.76$

$x4=4\ y4=25.14$

so

$y2-y1=24.38-24=0.38$

$y3-y2=24.76-24.38=0.38$

$y4-y3=25.14-24.76=0.38$

therefore

the answer is

the common difference is $0.38$

3 0

3 years ago

Read 2 more answers