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8 March, 20:05

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.

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Answers (2)
  1. 8 March, 20:20
    0
    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.
  2. 8 March, 20:26
    0
    This equation shows the total costs

    5.5a + 2.5p = 6.75

    This equation shows the total amount of pounds

    a + p = 1.5

    Here is the substitution method:

    a = 1.5 - p

    p = 1.5 - a

    feel free to substitute any one in

    i'll use 'p'

    5.5a + 2.5 (1.5 - a) = 6.75

    5.5a + 3.75 - 2.5a = 6.75

    3a = 3

    a = 1

    we know p = 1.5 - a

    p = 1.5 - 1

    p =.5

    therefore a = 1

    p = 2.5
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