Susan is buying black and green olives from the olive bar for her party. she buys 4 pounds of olives. black olives cost $3 a pound green olives cost $5 a pound she spends $15.50 how many pounds of each type of olive does she buy. write and solve a system of equations

Let number of pounds of black olive = x

Let number of pounds of green olive = y

Then total number of olive will be (x+y)

Given that she buys 4 pounds of olives. so we get equation

x+y=4

or x=4-y...(i)

Given that cost of 1 pound of black olive = $3

then cost of x pounds of black olive = 3x

Given that cost of 1 pound of green olive = $5

then cost of y pounds of green olive = 5y

which gives total cost = (3x+5y)

Given that "she spends $15.50" so we get equation:

3x+5y=15.50...(ii)

Now we just need to solve both equations.

Plug value of x from equation (i) into (ii)

3x+5y=15.50

3(4-y)+5y=15.50

12-3y+5y=15.50

12+2y=15.50

2y=15.50-12

2y=3.5

y=3.5/2

y=1.75

Now plug value of y into (i)

x=4-y=4-1.75=2.25

Hence final answer is given by:

system of equation is x=4-y, 3x+5y=15.50

Number of pounds of black olive = 2.25 pound

Number of pounds of green olive = 1.75 pound