In a football match 3 teams were competing...

Question

In a football match 3 teams were competing.. The 1st team scored 10 points more than the 2nd team, the 2nd team scored 5 points more than the 3rd team. If all 3 teams scored110 points overall, how many points did each team score?

Answer 1

Hi S,

I see that you are discovering word problems !   And translating word problems into precise, concise algebra notation is a very important skill.  Learn it well !

Let’s see, three teams are competing, so let’s call their scores A, B, and C.  Choose names that make sense and that you can remember.

Then, refer to your chart of algebra expressions and how they translate  (you do have a chart, don’t you?).

For example,

    the sum of a and b                               a  +  b

    the difference between a and b             a  -  b

    the product of a and b                           a  *  b

    the ratio of a to b                                  a  /  b

    is                                                            =

    a is more than b                                   a   >  b

    a is twice b                                           a = 2 * b

Add to this chart every day.

 

“The first team scored 10 points more than the 2nd team”      becomes   A  =  10  +  B

“The second team scored 5 points more than the 3rd team”     becomes    B  =  5  +  C

“All 3 teams scored 110 points overall”    becomes   A  +  B  + C  = 110

 

Much later, you will learn that if you have 3 variables and 3 independent equations, then you may solve for the 3 variables.   The easy method is called substitution.

            A                  +        B       +      C   =   110

        (10  +     B)      +  (5  + C )   +      C   =   110

        (10  + (5+C))   +  (5 + C)     +      C   =  110

        20 + 3*C  = 110

        3*C  =  90

        C = 30

 

Now, plug 30 in place of C in the second equation to solve for B:      B  =  5  +  C

Once you have found B, plug that answer into the first equation to solve for A:       A  =  10 + B

 

After all values are known, CHECK YOUR WORK !     A  +  B  +  C  must equal 110.   If not, you have an error.

If so, you have the correct answers !

 

Answer 2

Let A, B, and C = the three different teams.

Then:

A + B + C = 110

and we know that

B = A - 10
C = B - 5

so substituting into the first equation, we have

A + (A - 10) + (A - 10) - 5 = 110

combine like terms and solve:

3A - 25 = 110
3A = 135

A = 45
B = 35
C = 30