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anonymous

  • one year ago

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

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  1. mathstudent55
    • one year ago
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    This problem can be solved with a system of equations. Are you learning how to solve systems of equations?

  2. anonymous
    • one year ago
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    been a while cant quite remember how to do it

  3. mathstudent55
    • one year ago
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    First, we need to write the two equations. Then, we'll solve them.

  4. anonymous
    • one year ago
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    6x+2y=20 3x+5y=23 is that correct

  5. mathstudent55
    • one year ago
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    We need to choose two variables. Since most of the time we are used to using x and y as variables, let's use x and y. Let x = the cost per pound of jelly beans. Let y = the cost per pound of almonds.

  6. mathstudent55
    • one year ago
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    The first case we have is "For 6 pounds of jelly beans and 2 pounds of almonds, the total cost is $20." If jelly beans cost x dollars per pound, and you buy 6 pounds, how much does it cost?

  7. anonymous
    • one year ago
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    6x+2y=20 3x+5y=23 is that correct

  8. mathstudent55
    • one year ago
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    Yes, you are correct. Now you have the two equations for our system of equations. Now we need to solve the system of equations.

  9. mathstudent55
    • one year ago
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    We can use the substitution method. First, take the first equation you wrote, and divide the entire equation by 2. What do you get?

  10. mathstudent55
    • one year ago
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    6x + 2y = 20 Divide the entire equation by 2 to get: 3x + y = 10 Now we solve the equation for y: y = 10 - 3x Now we do the substitution step. Since y = 10 - 3x, where we see y in the second equation, we substitute y with 10 - 3x 3x + 5y = 23 3x + 5(10 - 3x) = 23 Simplify the parentheses with the distributive property: 3x + 50 - 15x = 23 Collect like terms on the left side: -12x + 50 = 23 Subtract 50 from both sides: -12x = -27 Divide both sides by -12: x = 2.25 Now that we know x, substitute x in the first original equation to find y. 6x + 2y = 20 6(2.25) + 2y = 20 13.5 + 2y = 20 2y = 6.5 y = 3.25 The price of jelly beans is $2.25 per pound, and the price of almonds is $3.25 per pound

  11. mathstudent55
    • one year ago
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    I have to go. Take your time to go over the solution. If you have questions, just ask, and I'll try to answer when I get back.

  12. anonymous
    • one year ago
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    ty i am looking iver to make sure i got it.. i have 5 like this

  13. mathstudent55
    • one year ago
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    yw

  14. anonymous
    • one year ago
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    Thanks for taking the time to explain this to me.. Your help got me a 100 on my final exam

  15. mathstudent55
    • one year ago
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    Wow. That's great. Congratulations.

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