So for this system, one equation will represent the number of fruit and the other equation will represent the combined total of the fruit. (Let x = apples and y = bananas):
[tex]x+y=20\\0.5x+0.75y=11.50[/tex]
Next, I will be using the substitution method to remove one of the variables. To do this, firstly subtract both sides by y in the first equation:
[tex]x=20-y\\0.5x+0.75y=11.50[/tex]
Next, since we know that x is equal to 20 - y, substitute it into the second equation and solve for y:
[tex]0.5(20-y)+0.75y=11.50\\10-0.5y+0.75y=11.50\\10+0.25y=11.50\\0.25y=1.50\\y=6[/tex]
Now that we have the value of y, substitute it into either equation to solve for x:
[tex]x+6=20\\x=14\\\\0.5x+0.75(6)=11.50\\0.5x+4.5=11.50\\0.5x=7\\x=14[/tex]
In short, Angelo bough 14 apples and 6 bananas.
