College Algebra

A gift store is making a mixture of almonds, pecans, and peanuts, which sells for $4.50 per pound, $3 per pound, and $4 per pound, respectively. The storekeeper wants to make 50 pounds of mix to sell at $4.38 per pound. The number of pounds of peanuts is to be three times the number of pounds of pecans. Find the number of pounds of each to be used in the mixture.

work so far:
x = almonds
y = pecans
z = peanuts

x = $4.50
y = $3
z = $4

Thank you.

  1. 0
asked by Gabbi
  1. you don't seem to be reading what is given. If you set up your x,y,z as you did, then

    x+y+z = 50
    y = 3z
    4.50x + 3y + 4z = 4.38*50

    posted by Steve
  2. To eliminate variables could I multiply the first equation by -4.50 and then add that equation to the third equation to eliminate x?

    Thank you.

    posted by Gabbi
  3. This one is easier to solve just using substitution:

    y=3z, so

    x+3z+z = 50
    4.50x + 3(3z) + 4z = 4.38*50

    Simplify those to get

    x + 4z = 50
    4.50x + 13z = 219

    Now, since x = 50-4z,
    4.50(50-4z)+13z = 219
    225-18z+13z = 219
    5z = 6

    z = 1.2
    y=3z = 3.6
    x=50-4z = 45.2

    This makes sense, since the final price is so close to the price of peanuts. Most of the mix will have to be peanuts.

    posted by Steve
  4. If you want to use elimination, arrange the equations so that x,y,z occur in order, and enter the coefficients into the array here:

    http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Mathematics

    Check my answer?? The bulk food section of a grocery store has two bins with different types of mixed nuts, The first bin contains Walnuts, peanuts and pistachios, The second bin contains pecans, almonds, Brazil Nuts and Walnuts,
  2. Math Help plz!!! Really need help.

    Use the Systematic Trial to solve this problem. Peanut-Pecan Problem Peanuts sell at $5/kg and pecans sell at $20/kg. Marika wants to make 30kg of a mixture of peanuts and pecans that will s ell at $10/kg/ How many kilograms of
  3. Algebra 2

    Given: 11-pound mixture of peanuts, almonds, and raisins Cost: peanuts - 1.5 per pound almonds - 3 per pound raisins - 1.5 per pound mixture: twice as many peanuts as almond; total cost of mixture is 21. a + p + r = 11 lbs a + 2a
  4. math

    A man sells a nut mixture consisting of 1/3 pecans and 2/3 cashews. Pecans cost 3 times as much as cashews. if a pund of the mixture costs him $0.40, how much did he pay for a pond of cashews? a pound of pecans?
  5. Math

    A candy store currently sells almonds for $8.50 per kilogram and peanuts for $4.50 per kilogram. It wants to create 20 kilograms of mixed nuts that will equivalently sell for $5.30 per kilogram. How many kilograms of almonds
  6. math

    A candy store currently sells almonds for $8.50 per kilogram and peanuts for $4.50 per kilogram. It wants to create 20 kilograms of mixed nuts that will equivalently sell for $5.30 per kilogram. How many kilograms of almonds
  7. Math

    The grocery store has bulk pecans on sale, which is great since you're planning on making 8 pecan pies for a wedding. How many pounds of pecans should you buy? First, determine what information you need to answer this question,
  8. Math

    A grocery store wants to make a mixture of nuts consisting of cashews and pecans. The cashews sell for $4 per pound while the pecans sell for $10 a pound. How many pounds of each nut must be mixed to produce a 6 pound mixture that
  9. Algebra

    A grocery store makes a 20-pound mixture of almonds and cashew nuts. The store charges $4 per pound for almonds and $5.50 per pound for cashews. The total value of the mixture is $92. Write a system to find how many pounds of each
  10. Algebra

    pecans priced at $5.85 per pound are mixed with almonds priced at $4.93 per pound to make a 40 pound mixture that will sell for $5.62 per pound. How many pounds of pecans and how many pounds of almonds must be used for this

More Similar Questions