The pairs of goldfish Tasha can buy for $20 are [tex](0,20), (1,17), (2,14),[/tex]
[tex](3,11),(4,8),(5,5),and (6,2)[/tex]
Step-by-step explanation:
To find the how many type of goldfish that Tasha can buy for $20 is the set of positive ordered pairs.
Let x denote the number of fancy goldfish.
Let y denote the number of common goldfish.
To find how much goldfish can Tasha buy for $20 is to substitute the value for x in the equation [tex]y=20-3x[/tex]
Now, substituting [tex]x=0[/tex] in [tex]y=20-3x[/tex], we get,
[tex]y=20[/tex]
The ordered pair is [tex](0,20)[/tex]
Similarly, substituting [tex]x=1[/tex],
[tex]y=20-3(1)\\y=20-3\\y=17[/tex]
For [tex]x=2[/tex],
[tex]y=20-6\\y=14[/tex]
For [tex]x=3[/tex],
[tex]y=20-9\\y=11[/tex]
For [tex]x=4[/tex],
[tex]y=20-12\\y=8[/tex]
For [tex]x=5[/tex],
[tex]y=20-15\\y=15[/tex]
For [tex]x=6[/tex],
[tex]y=20-18\\y=2[/tex]
Thus, the pairs of goldfish Tasha can buy for $20 are [tex](0,20), (1,17), (2,14),[/tex][tex](3,11),(4,8),(5,5),and (6,2)[/tex]
