Question

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. How many pounds of each type of olives does she buy? Write and solve a system of equations. Give the answer to in context of the problem.

Answer 1

She buy 0.5 pounds of black olives and 3.5 pounds of green olives.

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
`x.`

And the pounds of green olives be
`y.`

So, total pounds of olives:

`x+y=4`

`x=4-y` ........( 1 )

As, given the cost of black olives $3 a pound.

And cost of green olives $4 a pound.

Now, the total money spends:

`3x+4y=15.50`

Substituting the value of
`x` from equation (1) we get:

`3(4-y)+4y=15.50`

`12-3y+4y=15.50`

`12+y=15.50`

Subtracting both sides by 12 we get:

`y=3.5`

The green olives = 3.5 pounds.

Now, substituting the value of
`y` in equation (1):

`x=4-y\\x=4-3.5\\x=0.5\ pounds.`

The black olives = 0.5 pounds.

Therefore, she buy 0.5 pounds of black olives and 3.5 pounds of green olives.