# A \$2 raffle ticket offers a bonus \$1 early bird draw. 400 tickets were sold for the draw and a total of \$894 was collected from ticket sales. How many tickets were bought for \$2 and how many were bought for \$3? System of equations I know I have to make a system of equations and solve the variables but I am having trouble figuring out what the equations ( and variables) would be?

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Define the variables.
x = tickets bought for \$2
y = tickets bought for \$3

400 tickets were sold, so x + y = 400.

\$894 was collected.  x is worth \$2 each and y is worth \$3 each, so 2x + 3y = 894

x + y = 400
2x + 3y = 894

Solve the first equation for x.
x + y = 400
x = 400 - y

Now substitute this expression in for x in the second equation.
2x + 3y = 894
2(400 - y) + 3y = 894

Now solve for y.
2(400 - y) + 3y = 894
800 - 2y + 3y = 894
800 + y = 894
y = 94

Use this value to find x in the first equation.
x + y = 400
x + 94 = 400
x = 306

Solution:  {x = 306, y = 94}

You can check this answer by substituting both values into the second equation.
2x + 3y = 894
2 * 306 + 3 * 94 = 894
612 + 282 = 894
894 = 894
The solution is correct.

Solution:  {x = 306, y = 94}

306 tickets were bought for \$2 and
94 tickets were bought for \$3.

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