Writing a System of Equations from a word problem

Mickeyy21

New member
Joined
Feb 22, 2014
Messages
2
I am really struggling to get this topic down! I am a college freshmen and I am taking algebra.
Here is one of the practice problems I have:

"During the 1998-1999 Little League Season, the Tigers played 57 games. They lost 21 more games than they won. How many games did they win that season?" You have to make a system of equations using these steps:

1. Choose a value for x (or L).
2. Choose a value for y (or W).
3. Use the relationships given to make two equations.
4. Demonstrate how to solve the system of two equations using substitution.

I've found the answer to the question by subtracting 21 from 57 and getting 36, and then dividing 36 by 2 and getting 18. So they won 18 games, and I know how I got that answer, but I'm not sure how to write equations to solve the problem:confused:.

(57-21)÷2=18 18=wins, 57=total games and 39=losses(21+18)
 
Last edited:
"during the 1998-1999 little league season, the tigers played 57 games. They lost 21 more games than they won. How many games did they win that season?" you have to make a system of equations using these steps:

1. Choose a value for x (or l).
2. Choose a value for y (or w).
3. Use the relationships given to make two equations.
4. Demonstrate how to solve the system of two equations using substitution.
\(\displaystyle l+w=57\\l=w+21\)
 
I am really struggling to get this topic down! I am a college freshmen and I am taking algebra.
Here is one of the practice problems I have:

"During the 1998-1999 Little League Season, the Tigers played 57 games. They lost 21 more games than they won. How many games did they win that season?" You have to make a system of equations using these steps:

1. Choose a value for x (or L).
2. Choose a value for y (or W).
3. Use the relationships given to make two equations.
4. Demonstrate how to solve the system of two equations using substitution.

I've found the answer to the question by subtracting 21 from 57 and getting 36, and then dividing 36 by 2 and getting 18. So they won 18 games, and I know how I got that answer, but I'm not sure how to write equations to solve the problem:confused:.

(57-21)÷2=18 18=wins, 57=total games and 39=losses(21+18)

pka has given you the two equations you need:

Let

w = # games that Tiger won

l = # games that Tiger lost

l + w = 57 ← the Tigers played 57 games ..........................................(1)

l = w + 21 ← They lost 21 more games than they won .........................(2)

Eqn #2 gives you an expression for variable 'l'. Now "substitute" l from (2) into (1)

l + w = 57

(w +21) + w = 57 ← substituted for 'l' from (2)

2w + 21 = 57

2w = 57 - 21 = 36

w = 36/2 = 18

Using this value of 'w' into (2) we get

l = w + 21

l = 18 + 21 = 39

Now check - use these values of 'l' & 'w' into (1) & (2) and make sure the equations are satisfied with these values.
 
Last edited by a moderator:
Top