Question

Adult tickets to space city amusement park cost x dollars. Childrens tickets cost y dollars. The henson family bought 3 adult and 1 child ticket for $163. The Garcia family bought 2 adult and 3 child tickets for $174. Write equations to represent the Henson's cost and the Garcia's cost. Solve the system.

Answer 1

Henson family

`3x + y = 163`

Garcia family

`2x + 3y = 174`

Solution:


`y = 163 - 3x`
Substitute that into

`2x + 3(163 - 3x) = 174 \\ 2x + 489 - 9x = 174 \\ 7x = 315 \\ x = 45`

Substitute that into

`y = 163 - 3(45) \\ y = 28`

Answer: x = 45, y = 28

Hope this helps. - M

Answer 2

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Define x and y :
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Adult ticket = x
Children ticket = y

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Henson's family:
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3 adult and 1 child ticket for $163
⇒ 3x + y = 163

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Gracia's family:
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2 adult and 3 child tickets for $174
⇒ 2x + 3y = 174


------------------------------ Extra : To solve for x and y ------------------------------

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Solve for x and y :
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3x + y = 163 ----------------- (1)
2x + 3y = 174 ---------------- (2)

(1) x 3 :
9x + 3y = 489 ------------ (1a)

(1a) - (2) :
7x = 315
x = $45 ----------------- sub into (1)

3x + y = 163
3(45) + y = 163
135 + y = 163
y =$28


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Find the price of the tickets:
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Adult ticket = x = $45
Children ticket = y = $28