4
QuizMultiple Choice

Modeling with Matrices

Question 4 • GA-Advanced Algebra: Concepts and Connections CR

An office building has three air conditioning units, one for each office. Each unit runs only when employees are working. The tables below show the number of hours employees worked at each office over a three-month period and the total air conditioning electric costs for the entire office for each month. Number of Hours Worked Unit AUnit BUnit CJune184207276July174198264August168189242Total Air Conditioning Electric CostsJune$142.60July$135.96August$128.30How much does it cost to run Unit A per hour?

Answer
A
$0.19
B
$0.22
C
$0.24
D
$0.27

Explanation

Let a, b, and c be the hourly costs of Units A, B, and C. Comparing June with July gives 10a + 9b + 12c = $6.64; comparing July with August gives 6a + 9b + 22c = $7.66. Solving these equations together with July’s total, 174a + 198b + 264c = $135.96, gives a = $0.22 per hour. So the cost to run Unit A is $0.22, choice B.

AI-written and checked against the verified answer.

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