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a peanut company offers two different size cases containing some bags of almonds and some bags of peanuts. a small case contains 10 bags of almonds and 25 bags of peanuts and costs $75. A large case contains 40 bags of almonds and 60 bags of peanuts and costs $220. find the cost of in bag of peanuts

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MrsStrong

Answer:

Peanuts cost $2 a bag

Almonds cost $2.50 a bag

Step-by-step explanation:

To solve, write a system of equations using the information given.

  • "a small case contains 10 bags of almonds and 25 bags of peanuts for $75" translates to 10a+25p=75
  • "a large case comtains 40 bags of almonds and 60 bags of peanuts for $220" translates to 40a+60p=220

Solve by stacking the equations and performing elimination. To eliminate a variable, the coefficients must be the same. To make this so, we will multiply 10a+25p=75 by 4 to become 40a+100p=300. Now stack the equations and subtract:

40a+100p=300

40a+60p=220

----------------------------

0a + 40p=80

p=2 means peanuts cost $2 a bag.

Substitute p=2 into one equation to find a.

10a+25(2)=75

10a+50=75

10a=25

a=2.5 means almonds cost $2.50 a bag.

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