Word Problems solved by Elimination

Question

Stilt scored 5 points less than twice the number scored by Dunk. Together they scored a total of 43 points. How many points were scored by each player?

Answer 1

Stilt scored 5 points less than twice the number scored by Dunk. Together they scored a total of 43 points. How many points were scored by each player?

 

Answer: Let x points represent the number of points Stilt scored

Let y points represents represent the number of points scored by Dunk

Since Stilt scored 5 points less than twice the number of points scored by Dunk, then x = 2y-5 or x-2y=-5.................. that is equation 1

The sum of the points scored by both of them is 43, therefore x +y=43......... that is equation 2

Subtracting equation 2 from equation 1

x-2y=-5

x+y=43

then -3y=-48, therefore y=-48/-3, y=16

Since y points represents the number of points Dunk scored then Dunk scored 16 points

Substituting the value for y in equation then (x+y=43) then x+16 =43 and therefore x=43-16, hence x=27

Since x point represents Stilt's score then Stilt scored 27 points>

CHECKING BY SUBSTITUTING THE VALUES OF X AND Y IN THE EQUATION:

x + 2y =-5; 27 +2(16)=-5

x+y=43 ; 27 +16 = 43

 

Therefore Stilt score 27 points and Dunk scored 16 points.

 

Answer 2

Let x = points scored by Stilt and y = points scored by Dunk.

 

First, we'll write a system of equations:

 

"Stilt scored 5 points less than twice the number scored by Dunk" means

"Stilt scored 5 points less than twice y" means

"Stilt scored 5 points less than 2y" means

"Stilt scored 2y - 5" means

x = 2y - 5

 

"Together they scored a total of 43 points" means

"x + y = a total of 43 points" means

x + y = 43

 

Our system of equations is:

 

x = 2y - 5

x + y = 43

 

You want to solve by elimination, so let's rearrange that first equation a little:

 

x - 2y = -5

x + y = 43

 

Now, subtract the second equation from the first to eliminate the variable x:

 

    x - 2y = -5

- (x + y = 43)

------------------

    0 - 3y = -48

 

-3y = -48

y = -48/-3

y = 16

 

Now, plug y = 16 back into x + y = 43:

 

x + 16 = 43

x = 43 - 16

x = 27

 

This means that Stilt scored 27 points and Dunk scored 16 points.