Question

28. In a hockey match team ‘A’ scored one goal less than twice the number of
goals scored by team 'B?. If the product of the number of goals scored by
both the teams is 15, find the number of goals scored by each team.
​

Answer 1

Answer:

Team A=5 goals, Team B=3 goals

Step-by-step explanation:

Let A score y goals and B score x goals

From the question,

        y=2x-1

Also, xy=15

This gives us

$\frac{xy}{y} =\frac{15}{2x-1} \\x=\frac{15}{2x-1} \\15=x(2x-1)\\15=2x^2-x\\x^2-\frac{x}{2} =15/2\\x^2-\frac{x}{2} +(\frac{1}{4} )^2=15/2+(1/4)^2\\(x-1/4)^2=(120+1)/16\\x-1/4=\sqrt{121/16}=11/4\\x=12/4=3$

    Since xy=15 and x=3, y=5

Therefore team A scored 5 goals and team B scored 3 goals.

Answer 2

Answer:

goals of B=x

goals of A=2x-1

product of both is 15

I.e x(2x-1)=15

2x²-x-15=0

by using quadratic equation formulae

x=(-(-1)+‐((-1)²-4(2)(-15))^1/2)/2(2)

x=(1+‐(121)^1/2)/2(2)

(+‐ indicates +(or)-)

x=(1+‐(11))/4

x=3 (or) -5/2

negative goals is not possible so, x=3

by sub in eq.1

Goals scored by team B is 3

Goals scored by team A is 2(3)-1=5

HOPE IT HELPS