Question

A culinary club earns $843 from a dinner service. They sold 31 adult meals and 54 student meals. An adult meal costs $8 more than a student meal. What is the cost of an adult meal?

Answer 1

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: An adult meal costs $15.

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