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Oil Change \(+\) Oil Filter \(+\) Deluxe Air Filter \(= 42\) ----------------- (I)
Oil Change \(+\) Oil Filter \(+\) Standard Air Filter \(= 30\) --------------- (II)

(I) - (II)

Deluxe Air Filter \(-\) Standard Air Filter \(= 12\)

We are given that Deluxe Air Filter \(= 4*(\)Standard Air Filter\()\)

So, \(4*(\)Standard Air Filter\()\) \(-\) Standard Air Filter \(= 12\)

\(3*\)Standard Air Filter\(= 12\)

Standard Air Filter \(= 4\)

Answer is (B)
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Bunuel
An auto body shop charges $30.00 for an oil change, oil filter and standard air filter, but $42.00 for an oil change, oil filter and deluxe air filter. If the deluxe air filter costs four times as much as the standard air filter, how much does the standard air filter cost?

(A) $2.00
(B) $4.00
(C) $5.00
(D) $6.00
(E) $8.00

Given: An auto body shop charges $30.00 for an oil change, oil filter and standard air filter, but $42.00 for an oil change, oil filter and deluxe air filter. The deluxe air filter costs four times as much as the standard air filter.

Asked: How much does the standard air filter cost?

An auto body shop charges $30.00 for an oil change(oc), oil filter(of) and standard air filter (saf)

oc+of+saf=$30 (1)

42.00 for an oil change, oil filter and deluxe air filter.(daf)

oc+of+daf=$42 (2)

The deluxe air filter costs four times as much as the standard air filter.

daf=4saf (3)

(2) - (1)

daf - saf = 12 = 4saf - saf = 3saf
saf = $4
daf = $16

Standard Air Filter costs $4.

IMO B
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Bunuel
An auto body shop charges $30.00 for an oil change, oil filter and standard air filter, but $42.00 for an oil change, oil filter and deluxe air filter. If the deluxe air filter costs four times as much as the standard air filter, how much does the standard air filter cost?

(A) $2.00
(B) $4.00
(C) $5.00
(D) $6.00
(E) $8.00


We can let c, f, s and d be the cost of the oil change, oil filter, standard air filter and deluxe air filter, respectively, and create the equations:

c + f + s = 30

and

c + f + d = 42

Subtracting the first equation from the second, we have:

d - s = 12

Since the deluxe air filter costs four times as much as the standard air filter, we have d = 4s. Substituting 4s for d in d - s = 12, we have:

4s - s = 12

3s = 12

s = 4

Answer: B
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