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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

A charitable organization in Norwood is hosting a black tie benefit. Yesterday, the organization sold 37 regular tickets and 45 VIP tickets, raising $7,940. Today, 75 regular tickets and 45 VIP tickets were sold, bringing in a total of $10,410. How much do the different ticket types cost?

Write a system of equations to describe the situation below solve using elimination and fill in the blanks A charitable organization in Norwood is hosting a bla class=

Respuesta :

37x + 45y = 7940
75x + 45y = 10,410

Since 45y is in both equations we can more easily transfer from first equation to 2nd equation.

In the first equation, subtract 37x from each side and you have 45y = 7940 - 37x. Replace the 45y in the second equation with (7940 - 37x).

Now you have 75x + (7940 - 37x) = 10,410

Simplify by combining 75x - 37x and you have 38x + 7940 = 10,410

Subtract 7940 from both sides and you have 38x = 2470.

Divide both sides by 38 and you have x = 65

To solve for y, take you first equation (or even the second one) and substitute c for 65.

(37 x 65) + 45y = 7940
2405 + 45y = 7940

Subtract 2405 from each side.

45y = 5535

Divide each side by 45 and you have y = 123

Regular tickets = $65
VIP tickets = $123

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