Alicia and sarah are at the supermarket. alicia wants to get peanuts from the bulk food bins and sarah wants to get almonds. the almonds cost $5.50 per pound and the peanuts cost $2.50 per pound. together they buy 1.5 pounds of nuts. if the total cost is $6.75, how much did each girl get? state the system of equations you are using to solve solve for both almonds and peanuts.

Let p = weight of peanuts.
Let a = weight of almonds.

They bought a total of 1.5 lb, so the first equation is

p + a = 1.5

Now we deal with the cost.

p pounds of peanuts cost 2.50p.
a pounds of almonds cost 5.50a.
The total cost was $6.75, so this gives us the second equation.

2.5p + 5.5a = 6.75

We put the two equations together, and we have a system of equations.

p + a = 1.5
2.5p + 5.5a = 6.75

We can use substitution. Solve the first equation for p and substitute in the second equation.

p = 1.5 - a

2.5(1.5 - a) + 5.5a = 6.75

3.75 - 2.5a + 5.5a = 6.75

3a + 3.75 = 6.75

3a = 3

a = 1

Now we substitute a = 1 in the original first equation to find p.

p + a = 1.5

p + 1 = 1.5

p = 0.5

They bought 1 lb of almonds and 0.5 lb of peanuts.