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At a travel agency, the cost of a trip to Mexico is $350 for an adult and $200 for a child. One month, the agency sold 50 trips. Of these trips, Y trips were for children. The travel agency collected C dollars from selling all 50 trips. Express Y in terms of C.

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Ashraf82

Y = [tex]\frac{350}{3}[/tex] - [tex]\frac{1}{150}[/tex] C

Step-by-step explanation:

At a travel agency

  • The cost of a trip to Mexico is $350 for an adult and $200 for a child
  • The agency sold 50 trips, of these trips Y trips were for children
  • The travel agency collected C dollars from selling all 50 trips

Assume that X trips were for adult

∵ The agency sold 50 trips

∵ There were Y trips for children

∵ there were X trips for adult

∴ X + Y = 50

- Subtract Y from each side

∴ X = 50 - Y ⇒ (1)

∵ The cost of the trip of one adult = $350

∵ The cost of the trip of one child = $200

∵ The travel agency collected C dollars from selling all trips

∴ C = 350 X + 200 Y ⇒ (2)

Substitute X in equation (2) by equation (1)

∵ C = 350(50 - Y) + 200 Y

∴ C = 350(50) - 350(Y) + 200 Y

∴ C = 17500 - 350 Y + 200 Y

- Add like terms

∴ C = 17500 - 150 Y

Now lets find Y in terms of C

∵ C = 17500 - 150 Y

- Add 150 Y in both sides

∴ C + 150 Y = 17500

- Subtract C from both sides

∴ 150 Y = 17500 - C

- Divide each term by 150

∴ Y = [tex]\frac{350}{3}[/tex] - [tex]\frac{1}{150}[/tex] C

Y = [tex]\frac{350}{3}[/tex] - [tex]\frac{1}{150}[/tex] C

Learn more:

You can learn more about linear equations in brainly.com/question/2115716

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