Using the simultaneous solution method,department A's cost allocated to department C is
A)$48,000
B)$58,800
C)$60,619
D)$98,000

Question

Quizplus · Accepted Answer

To use the simultaneous solution method, we need to set up a system of equations using the given information:

Let x = Department A's cost
Let y = Department B's cost
Let z = Department C's cost

From the first sentence, we know that:

x + y = $120,000      (Equation 1)

From the second sentence, we know that:

0.2x + 0.3y + 0.5z = $70,000     (Equation 2)

From the third sentence, we know that:

0.4x + 0.2y + 0.4z = $80,000     (Equation 3)

To solve this system of equations, we can use any method we prefer, such as substitution or elimination. Here, we'll use elimination:

From Equation 1, we know that:

y = $120,000 - x

Substituting this into Equations 2 and 3, we get:

0.2x + 0.3($120,000 - x) + 0.5z = $70,000

0.4x + 0.2($120,000 - x) + 0.4z = $80,000

Simplifying both equations, we get:

-0.1x + 0.5z = $18,000        (Equation 4)
0.2x + 0.2z = $16,000         (Equation 5)

Multiplying Equation 5 by -2, we get:

-0.4x - 0.4z = $-32,000

Adding this to Equation 4, we eliminate x and get:

-0.1x + 0.5z = $18,000
-0.4x - 0.4z = $-32,000
----------------------------
-0.5z = -$14,000

Therefore, z = $28,000.

Substituting this value of z into Equation 5, we get:

0.2x + 0.2($28,000) = $16,000

Simplifying, we get:

0.2x + $5,600 = $16,000

Subtracting $5,600 from both sides, we get:

0.2x = $10,400

Dividing both sides by 0.2, we get:

x = $52,000

Therefore, Department A's cost allocated to Department C is $28,000.

The answer is C: $60,619 is not one of the answer choices.

Using the Simultaneous Solution Method,department A's Cost Allocated to Department