Answer:
She buy 0.5 pounds of black olives and 3.5 pounds of green olives.
Step-by-step explanation:
Given:
Susan is buying black and green olives from the Olive bar for her party. She buys 4 pounds of olives.
Black olives cost three dollars a pound. Green olives cost five dollars a pound.
She spends $15.50.
Now, to find the pounds of olives she buy.
Let the pounds of black olives be [tex]x.[/tex]
And the pounds of green olives be [tex]y.[/tex]
So, total pounds of olives:
[tex]x+y=4[/tex]
[tex]x=4-y[/tex] ........( 1 )
As, given the cost of black olives $3 a pound.
And cost of green olives $4 a pound.
Now, the total money spends:
[tex]3x+4y=15.50[/tex]
Substituting the value of [tex]x[/tex] from equation (1) we get:
[tex]3(4-y)+4y=15.50[/tex]
[tex]12-3y+4y=15.50[/tex]
[tex]12+y=15.50[/tex]
Subtracting both sides by 12 we get:
[tex]y=3.5[/tex]
The green olives = 3.5 pounds.
Now, substituting the value of [tex]y[/tex] in equation (1):
[tex]x=4-y\\x=4-3.5\\x=0.5\ pounds.[/tex]
The black olives = 0.5 pounds.
Therefore, she buy 0.5 pounds of black olives and 3.5 pounds of green olives.
