A store is having a sale on almonds and jelly beans. For 6 pounds of almonds and 2 pounds of jelly beans, the total cost is 20. For 3 pounds of almonds and 5 pounds of jelly beans, the total cost is 23. Find the cost for each pound of almonds and each pound of jelly beans.

Each pound of almonds is $2.25 and each pound of jelly beans is $3.25

Step-by-step explanation:

Create a system of equations where a is the cost for a pound of almonds, and j is the cost for a pound of jelly beans

6a + 2j = 20

3a + 5j = 23

Solve by elimination by multiplying the bottom equation by -2, then adding them together

6a + 2j = 20

-6a - 10j = -46

Add them together, then solve for j

-8j = -26

j = 3.25

Solve for a by plugging in 3.25 as j into one of the equations

6a + 2j = 20

6a + 2(3.25) = 20

6a + 6.5 = 20

6a = 13.5

a = 2.25

So, each pound of almonds is $2.25 and each pound of jelly beans is $3.25

i think it's eleven too, don't woosh me here, but according to the "experts" it's 2.

the proof starts from the peano postulates, which define the natural

numbers n. n is the smallest set satisfying these postulates:

  p1.   1 is in n.

  p2.   if x is in n, then its "successor" x' is in n.

  p3.   there is no x such that x' = 1.

  p4.   if x isn't 1, then there is a y in n such that y' = x.

  p5.   if s is a subset of n, 1 is in s, and the implication

      (x in s => x' in s) holds, then s = n.

then you have to define addition recursively:

  def: let a and b be in n. if b = 1, then define a + b = a'

      (using p1 and p2). if b isn't 1, then let c' = b, with c in n

      (using p4), and define a + b = (a + c)'.

then you have to define 2:

  def:   2 = 1'

2 is in n by p1, p2, and the definition of 2.

theorem:   1 + 1 = 2

proof: use the first part of the definition of + with a = b = 1.

      then 1 + 1 = 1' = 2   q.e.d.

note: there is an alternate formulation of the peano postulates which

replaces 1 with 0 in p1, p3, p4, and p5. then you have to change the

definition of addition to this:

  def: let a and b be in n. if b = 0, then define a + b = a.

      if b isn't 0, then let c' = b, with c in n, and define

      a + b = (a + c)'.

you also have to define 1 = 0', and 2 = 1'. then the proof of the

theorem above is a little different:

proof: use the second part of the definition of + first:

      1 + 1 = (1 + 0)'

      now use the first part of the definition of + on the sum in

      parentheses:   1 + 1 = (1)' = 1' = 2   q.e.d.

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