Answer:
24 Home games
Step-by-step explanation:
let [tex]x[/tex] denote the number of home games played, and [tex]y[/tex] denote the number of home games played. We are given the total number of games played as 49
and total wins as 26.
The problem can be expressed in equation form as:[tex]\frac{2}{3}x+\frac{2}{5}y=26[/tex]...[tex]eqtn1[/tex]
Total games is expressed as [tex]x+y=49[/tex]...[tex]eqtn2[/tex]
Rewrite equation 1 to remove fractions:
[tex]\frac{2}{3}x+\frac{2}{5}y=26\\=>5x+3y=195\\[/tex]
Solve for x to obtain total home games played.
Making [tex]x[/tex] the subject in eqtn 2:
[tex]x=49-y[/tex]
Substitute for [tex]x[/tex] in eqtn1:
=>
[tex]5(49-y)+3y=195\\-5y+3y=195-245\\-2y=-50\\y=25[/tex]
To obtain [tex]x[/tex], replace y value in eqtn2:
[tex]x+y=49\\y=25\\Therefore\\x=49-25\\x=24[/tex]
Home games played is 24
