ian
16. There are 3 adults for
every 8 children at a
birthday party. If there are
a total of 55 people at the
party, how many adults are
there?

15adults

Step-by-step explanation:

Ratio of Children : Adult = 8 : 3

Number of children = 8x

Number of Adult = 3x

8x + 3x =55

11x = 55

x = 55/11

x = 5

Number of Adults = 3x = 3*5 = 15

40 adults

Step-by-step explanation:

Let x:y represent the ratio of children to adults. As of now, x:y is 3:8.

To solve this problem, all we need to do is find a solution where x + y = 55. Let's begin by using the guess-and-check method.  

First, I will multiply the ratio by 2.

When x = 6, y = 16

6 + 16 = 22

Not applicable; I need higher numbers

Next, I'll multiply the ratio by 4.

When x = 12, y = 32.

12 + 32 = 44

Not applicable, I need slightly higher numbers

I'll multiply the ratio by 5.

When x = 15, y = 40

15 + 40 = 55

Since 55 is the total number of people, 15 children and 40 adults is the correct answer. Therefore, the total number of adults is 40.

number one is the correct answer

step-by-step explanation: dogs and cats are mentioned, no other animals

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3