Need to solve using Elimination, Substitution and Graphing. Pens are x and Pencils are y.

Question

 

Penelop's Printing Press Promptly sold 5-cent pencils and 10-cent pens to the public. It sold 25 writing utensils and took in $2.00 in sales. How many pens and pencils did Penelop's Printing sell?

Answer 1

Let the number of pencils be x and the owns be y then

 

Since the total number of worrying utensils is 25 we get

 

x+y=25

 

Now we also know the total in sales was $2 meaning the sum of the sales of pens and pencils is equal to 2

 

5x +10y  = 200 

 

now solve these 2 equations 

 

I am going to use elimination multiply equation 1 by -5 we get

 

-5x - 5y = -125 

 

Now add this to the second equation to get

 

5y = 75

 

Y = 15

 

Now we can find x by substituting this value into the first equation

 

x = 25 - 15

 

= 10

 

We have 10 pencils and 15 pens. 

 

Answer 2

Dear Seyer,

Elimination

.05y+.10X=$2 Multiply the bottom equation by -.10.
y + X =25


.05y+.10X=$2 Add both equations together to eliminate one variable.
-.10y +-.10 X =-2.5
-.05Y= -.5 Divide both sides of the equation by "-.05."

Y= -.5/-.05 =10 Now substitute Y=10 to find "X."

Y+X=25 10+X=25 X=25-10=15 (15,10)


Graphing


Solve for "Y" in both equations:

.05Y= -.10X +2 Divide every term by the number next to "Y."

.05/.05 Y = -.10/.05 + 2/.05 Y= -2X + 40

and X+Y =25, so subtract "X" from both sides of equation.

Y= -X +25


Now enter both of these equations in the graphing mode, Function 1, Y=

Y= -2X + 40 Y= -X +25

Then you press GRAPH. However, you won't get a good picture unless you change the WINDOW. Go to

WINDOW, second function. Change X-max to 20, so you can see where the lines intersect each other.

Next, You can see where the lines intersect by pressing 2nd TRACE; then press number 5 for intersect. Next, press

the enter button before the intersection point on the graph. Then the calculator will ask you to make another guess.

Press enter again right after the intersection point. The display will then tell you exactly what the intersection point is

at (15,10).

Substitution

.05Y +.10X =2

Y + X=25 Solve for "Y" in the second equation. Y= 25-X. Then

substitute it into the first equation. .05(25-X) +.10X=2 Use distributive property.

1.25- .05X + .10X =2 Subtract -1.25 from both sides.

-.05X +.10X= .75 Collect like terms.

.05X= .75 Divide both sides by .05

X= .75/.05 =15

Substitute "X" value into second equation: Y + (15)=25 Solve for "Y."

Y=25-15=10 (15,10)
If I have helped, please give me a thumbs up.
Susan C.