Question

Blake is a member of a golf club. When he became a member, he deposited money into his club account. For each round of golf that he plays at the club, a fixed amount is deducted from his account. If y represents the amount, in dollars, left in his account after playing x rounds, which of the following situations is represented by the table below?

Rounds Played 2 4 6 8
Amount Remaining $280 $240 $200 $160
A.
Blake's account initially had $280, which is decreasing at the rate of $20 per round.
B.
Blake's account initially had $280, which is decreasing at the rate of $40 per round.
C.
Blake's account initially had $320, which is decreasing at the rate of $40 per round.
D.
Blake's account initially had $320, which is decreasing at the rate of $20 per round.
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Answer 1

D) Blake's account initially had $320, which is decreasing at the rate of $20 per round.

Explanation:

Here, according to the question:

x: The total number of golf rounds played

y: Represents the amount, in dollars, left in his account after playing x rounds

Let as assume A is the amount deposited initially.

y = A - n x here n : rate of each round played

Also, here

if x = 2, then y = 280

if x =4, then y = 240

If x = 2 and y = 280, then:

y = A - n x ⇒ 280 = A - 2 n ... (1)

If x = 4 and y = 240, then:

y = A - n x ⇒ 240 = A - 4 n ... (2)

Solving (1) and (2) by (1) - (2), we get:

40 = 2 n or, n = 20

Putting n = 20 in 280 = A - 2 n, we get: A = 280 + 2(20) = 320

⇒ A = $320, n = $20

⇒ The amount initially deposited is $320 and the rate per round is $20

Hence ,Blake's account initially had $320, which is decreasing at the rate of $20 per round.