Jacobs school is selling tickets to a fall musical. First day of ticket sales the school sold 28 tickets. If adult tickets cost \$8 each and child tickets cost \$5, how many adult and child tickets were sold? Total ticket sales: \$176
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MathFanatic2000 6 months ago
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12 adult tickets, 16 child tickets

Step-by-step explanation:

x is the amount of adult tickets
y is the amount of child tickets
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lets make 2 equations:
1)    x + y = 28
2)   8x + 5y = 176
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now we can substitute either x or y into the second equation so that we only have to deal with one variable at once.

x + y = 28
subtract y from each side:
x + y - y = 28 - y
which gives you:
x = 28 - y
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Then we plug that into the second equation, which will give us:

8(28 - y) + 5y = 176

now you want to expand 8(28 - y), so you use the distributive property.

8(28 - y) = 8*28 - 8*y = 224 - 8y

now that we have solved that, plug it back into the equation:

224 - 8y + 5y = 176

subtract 224 from each side:

224 - 8y + 5y - 224 = 176 -224

which gives us:
-3y = -48

now if you multiply each side by ( -1 ) you get:
3y = 48

now divide both sides by 3 and you get:
y = 48 / 3

48 / 3 is 16

y = 16
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now plug y = 16 into equation 1

equation 1 was x + y = 28

plug 16 in for y which gives us:

x + 16 = 28

subtract 16 from both sides

x + 16 - 16 = 28 - 16

Which finally gives us
x = 12
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Remember:
x is the amount of adult tickets
y is the amount of child tickets

x = 12 means that 12 adult tickets were sold
y = 16 means that 16 child tickets were sold
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