Jim and abby each bought burgers and fries from the concession stand at the fair. jim bought 3 burgers and 2 orders of fries for $17. abby bought 2 burgers and 4 orders of fries for $18. how much did it cost for each burger? how did it cost for each order of fries?

The price of each burger is $4

The price of each order of fries is $2.5

Step-by-step explanation:

* Lets explain how to change the story problem to equations

- Jim bought 3 burgers and 2 orders of fries for $17

- Abby bought 2 burgers and 4 orders of fries for $18

- Assume that the price of one burger is x and one order of fries is y

* Lets write two equations represents Jim and Abby orders

∵ Jim bought 3 burgers and 2 orders of fries for $17

∴ 3x + 2y = 17 ⇒ (1)

∵ Abby bought 2 burgers and 4 orders of fries for $18

∴ 2x + 4y = 18 ⇒ (2)

* Lets solve the two equations by the elimination method

- Multiply equation(1) by -2 to eliminate y

∵ -2(3x) + -2(2y) = -2(17)

∴ -6x + -4y = -34 ⇒ (3)

- Add equations (2) and (3)

∴ -4x + 0 = -16

∴ -4x = -16

- Divide both sides by -4

∴ x = 4

- Substitute the value of x in equations (1) or (2) to find y

∵ 3x + 2y = 17

∴ 3(4) + 2y = 17

∴ 12 + 2y = 17

- Subtract 12 from both sides

∴ 2y = 5

- Divide the both sides by 2

∴ y = 2.5

∵ x represent the price of each burger

∴ The price of each burger is $4

∵ y represents the price

  of an order of fries

∴ The price of each order of fries is $2.5

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