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A store is having a sale on walnuts and chocolate chips. For 7 pounds of walnuts and 9 pounds of chocolate chips, the total cost is $37. For 5 pounds of walnuts. and 3 pounds of chocolate chips, the total cost is $17. Find the cost for each pound of walnuts and each pound of chocolate chips.​

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mhanifa

Answer:

  • Walnuts  cost $1.75, chocolate chips cost $2.75

Step-by-step explanation:

Let the costs be:

  • Walnuts - x
  • Chocolate chips - y

Set equations as per question

For 7 pounds of walnuts and 9 pounds of chocolate chips, the total cost is $37:

  • 7x + 9y = 37

For 5 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $17:

  • 5x + 3y = 17

Solve the system by elimination

Multiply the second equation by 3 and subtract the first equation, solve for x:

  • 3(5x + 3y) - (7x + 9y) = 3(17) - 37
  • 15x + 9y - 7x - 9y = 51 - 37
  • 8x = 14
  • x = 14/8
  • x = 1.75

Find the value of y:

  • 7*1.75 + 9y = 37
  • 12.25 + 9y = 37
  • 9y = 37 - 12.25
  • 9y = 24.75
  • y = 24.75/9
  • y = 2.75

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