The culinary club earned $843 in all. They sold 31 adult meals (setting the variable as a), and 54 student meals (setting the variable as x).
843 = 31a + 54x
An adult meal costs $8 more than a student meal:
a = 8 + x
Your system of equation is:
843 = 31a + 54x
a = 8 + x
Solve. Note that 8 + x = a. Plug in 8 + x for a in the first equation
843 = 31(8 + x) + 54x
Simplify. Solve with PEMDAS. (Parenthesis, Exponents (& roots), Multiplication, Division, Addition, Subtraction). Remember that you can only combine like terms (terms with the same number of variables).
First, distribute 31 to all terms within the parenthesis.
31(8 + x) = 248 + 31x
843 = 248 + 31x + 54x
Simplify. Combine like terms
843 = 248 + (31x + 54x)
843 = 248 + 85x
Isolate the x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 248 from both sides.
843 (-248) = 248 (-248) + 85x
843 - 248 = 85x
595 = 85x
Isolate the x. Divide 85 from both sides
(595)/85 = (85x)/85
x = 595/85
x = 7
A student meal costs $7.
Plug in 7 for x in one of the equations:
a = 8 + x
a = 8 + (7)
Simplify
a = 15
An adult meal costs $15.
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Check: Plug in $7 for student meal, and $15 for adult meal
843 = 31a + 54x
843 = 31(15) + 54(7)
Simplify. Remember to follow PEMDAS
843 = 465 + 378
Add
843 = (465 + 378)
843 = (843) True
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Answer: <em>An adult meal costs $15</em>.
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