Find all 3-digit numbers which are 19 times the sum of their digits.

The 3 digit numbers are;

171, 152, 133, 114, 285, 266, 247, 228, 209, 399

Step-by-step explanation:

Let the 3 digit number be xyz

Since x is the Hundreds digit, y is the tens digit and z is the unit digit, we have;

100x, 10y and z

We are told the sum of this is equal to 19 times the sum of their digits.

Thus;

100x + 10y + z = 19(x + y + z)

100x + 10y + z = 19x + 19y + 19z

This gives;

81x - 9y - 18z = 0

Divide through by 9 to get;

9x - y - 2z = 0

x = (2z + y)/9

Now, we will need to select values of z and y between 0 to 9 in such a way that (2z + y) is divisible by 9 and in such a way that x > 0 but ≤ 10

The possible solutions are;

At z = 1, y = 7 and x = 1

At z = 2, y = 5 and x = 1

At z = 3, y = 3 and x = 1

At z = 4, y = 1 and x = 1

At z = 5, y = 8 and x = 2

At z = 6, y = 6 and x = 2

At z = 7, y = 4 and x = 2

At z = 8, y = 2 and x = 2

At z = 9, y = 0 and x = 2

At z = 9, y = 9 and x = 3

Compiling all these, the 3 digit numbers are;

171, 152, 133, 114, 285, 266, 247, 228, 209, 399

(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

steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.