use elimination to solve. For a production of sweeney Todd in Las Vegas, orchestra seats cost $42 and mezzanine seats cost $25.

Question

3 years ago

5

If a group of 14 people show up and spend a total of $486, how many of each kind of seat did they buy? please help!

1 answer:

lidiya [134] · Answer 1 · 2021-12-31T11:29:05+03:00

They bought 8 orchestra seats and 6 mezzanine seats.

Step-by-step explanation:

Cost of one orchestra seat = $42

Cost of one mezzanine seat = $25

No. of people = 14

Amount spent = $486

Let,

x be the number of orchestra seats

y be the number of mezzanine seats

According to given statement;

x+y=14 Eqn 1

42x+25y=486 Eqn 2

Multiplying Eqn 1 by 25;

$25(x+y=14)\\25x+25y=350\ \ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2 to eliminate y;

$(42x+25y)-(25x+25y)=486-350\\42x+25y-25x-25y=136\\17x=136$

Dividing both sides by 17

$\frac{17x}{17}=\frac{136}{17}\\x=8$

Putting x=8 in Eqn 1

$8+y=14\\y=14-8\\y=6$

They bought 8 orchestra seats and 6 mezzanine seats.

Keywords: linear equation, elimination method

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