Algebra anyone?

Question

Can anyone explain this question to me?

Use a letter to represent the unknown number and write the problem as an equation. Then, solve the equation.

In a cricket league, teams get 5 points for a win, 3 points for a draw, and 0 points for a defeat. After 20 matches, Mathstown have 80 points. They have only had 2 defeats. How many of their matches have been draws?


Anyone have any clue how to write that as an equation and why?

xxjes

Answer 1

Let W = # of wins
Let D = # of draws.
You know defeats = 2

They played 20 matches, so
W + D + 2 = 20
W + D = 18
W = 18 - D

And they have 80 points, so:
5W + 3D = 80
5(18-D) + 3D = 80
90 - 5D + 3D = 80
10 = 2D
D = 5 draws,
W + 5 + 2 = 20
so W = 13 wins

Answer 2

Let w = no. of wins.
Let t = no. of ties (draws).
Let d = no. of defeats.
Let p = no. of points.

Using 5 points for a win, 3 points for a tie, and 0 points for a defeat gives p = 5w + 3t.

Write down what we know:
After 20 matches gives w + t + d = 20.
Mathstown has 80 points gives p = 80 = 5w + 3t.
They have only had 2 defeats gives w + t + 2 = 20 or w + t = 18.

That gives two equations and two unknowns. Do some substitution:
w + t = 18 or w = 18 - t.
Substitute into 80 = 5w + 3t to get 80 = 5(18 - t) + 3t.

Now solve:
80 = 90 - 5t + 3t
10 = 2t
t = 5

5 draws

Answer 3

Let D be the number of draws, W be the number of wins, L be the number of losses, M be the number of matches, and P be the number of points:

P = 5*W + 3*D; M = W + L + D.

You're told that M = 20 and L = 2 ==> 20 = W + 2 + D ==> 18 = W + D ==> W = 18 - D.
You're also told that P = 80 ==> 80 = 5*W + 3*D = 5*(18 - D) + 3*D
==> 80 = 90 - 5D + 3D = 90 - 2D ==> 2D = 10 ==> D = 5.

Check: D = 5 ==> W = 13 ==> P = 13*5 + 5*3 = 65 + 15 = 80.

Done.

Answer 4

You are told that there were 20 matches, 2 of which were lost, so we're left with 18 matches that were either won or drawn.

Suppose I use the letter "d" to denote the number of matches drawn. With that convention, the number of victories is therefore:

number of victories: 18 - d

That's not yet the equation you want, but we're getting there! We want to write an equation about the number of points. The team got 80 points in total; that is made up of 3 points for each draw (3 * d); and also 5 points for each win (5 * (18-d), according to expression above):

total of points: 80 = 5 * (18-d) + 3 * d

That is an expression containing only one unknown: the number of draws "d". Let's simplify the expression a little:

80 = 5*18 - 5*d + 3*d
80 = 90 - 2*d
10 = 2*d
5 = d

There were 5 draws.

Answer 5

5W + 3D = 80 points
W is # of wins
D is # of draws

W + D + 2 = 20
2 represents the number of defeats and 20 is the total number of games

Now we can take that equation and solve for D (or W)
D = 18 - W

Substitute into the first equation

5W + 3(18 - W) = 80

5W + 54 - 3W = 80

2W = 26

W = 13

D = 18 - 13

D = 5

13 Wins, 5 Draws, 2 Defeats

Answer 6

They have had 20 matches. Of these the 2 defeats contributed nothing to their score, so consider the 18 matches in which they scored.

Let the number of matches they won be w

if they played w winning matches and 18 scoring matches, they played (18-w) drawn matches

Each winning match is worth 5 points. So w winning matches is worth 5w points.

Each drawn match is worth 3 points. So (18-w) drawn matches is worth 3(18-w) points

Going back to what they tell you in the question, the points from their drawn matches + points from their winning matches = 80

So you can create the equation

5w + 3(18-w) = 80.......multiply out the bracket

5w + 54 -3w = 80.....work out the ws and subtract 54 from each side

2w = 26

w = 13

They won 13 matches, they lost 2 matches (told in the question)

so they drew 20-15 =5 matches

Quick check

5 x 13 = 65

3 x 5 = 15 .....add these = 80 .......it works!

Answer 7

Let x be the number of victories and y be the number of draws.
So in eighteen matches they got 80 points. Hence x+y=18 and
5x+3y=80. You solve and get x=13 and y =5.

Answer 8

W = # of wins
D = # of draws

W + D + 2 = 20 {the number of matches}

5W + 3D = 80 {the number of points}

Solve this system of two equations in two unknowns.

Answer 9

w = win
d = draw
l = loss
w + l + d = 20 (l = 2)
w + d = 18 *** (use this to solve for w or d)
w = 18 - d ..... d = 18 - w

5(w) + 3(d) = 80 (5 for win + 3 for draw = 80 pts)
5(18 - d) + 3d = 80
90 - 5d + 3d = 80
-2d = -10
d = 5 ........ if d=5, then 18 - 5 = 13 (wins)

13 wins = 65pts
5 draws= 15
0 loss = 0

total of 80 pts

Answer 10

Let x = number of draws
18-x then = number of draws

5(18-x)= number of points from wins
3x= number of points from draws

5(18-x) + 3x = 80
90-5x+3x=80
-2x=10
x=5
5 draws
13 wins

So, the team won 13 matches, had draws in 5, and lost 2.