The admission fee at an amusement park is $2.50 for children and $5.80 for adults. On a certain day, 343 people entered the park, and the admission fees collected totaled $1369. How many children and how many adults were admitted?

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absor201 absor201 · Answer 1 · 2020-01-09T11:48:29+01:00

188 children and 155 adults were admitted that day.

Step-by-step explanation:

Given,

Cost of one children admission = $2.50

Cost of one adult admission = $5.80

Number of people entered = 343

Total admission fees collected = $1369

Let,

Number of children admission = x

Number of adult admission = y

According to given statement;

x+y=343 Eqn 1

2.50x+5.80y=1369 Eqn 2

Multiplying Eqn 1 by 2.50

[tex]2.50(x+y=343)\\2.50x+2.50y=857.50\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](2.50x+5.80y)-(2.50x+2.50y)=1369-857.50\\2.50x+5.80y-2.50x-2.50y=511.50\\3.30y=511.50[/tex]

Dividing both sides by 3.30

[tex]\frac{3.30y}{3.30}=\frac{511.50}{3.30}\\y=155[/tex]

Putting y=155 in Eqn 1

[tex]x+155=343\\x=343-155\\x=188[/tex]

188 children and 155 adults were admitted that day.

Keywords: linear equation, subtraction

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