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A museum sells three types of tickets, including those for seniors, adults, and children. On a Tuesday morning, the museum sells 164 tickets. The number of adult tickets sold was three times as many as senior tickets sold, and the number of child tickets sold was 10 more than the number of adult tickets sold. How many of each type of ticket did the museum sell on Tuesday morning?

Respuesta :

The number of senior, adults and children tickets sold are 22, 76 and 66 respectively.

The museum sells three types of tickets, including those for seniors, adults and children.

On Tuesday morning the  museum sold 164 tickets. Therefore,

  • Total ticket sold  = 164

Let

x = number of senior ticket sold.

The number of adult tickets sold was three times as many as senior tickets sold.

Equation for adult  ticket sold

  • 3x

The number of child tickets sold was 10 more than the number of adult tickets sold. Therefore,

Equation for child ticket sold

  • 10 + 3x

Total ticket sold = 3x + 10 + 3x + x

164 = 7x + 10

154 = 7x

x = 154 / 7

x = 22

Therefore,

number of senior ticket sold = 22

number of adult tickets sold = 3 (22) = 66

number of child tickets sold = 10 + 3(22) = 76

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