题目信息
At a certain university recreation center, a member can receive a 30-minute massage, a 60-minute massage, or a 90-minute massage, and is charged $0.50 per minute for each massage. A member receiving a massage is charged the same fixed amount for each additional service, such as nutrition advice or a fitness evaluation. At this center, what is the total charge to a member for a 60-minute massage and 3 additional services?
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D:EACH statement ALONE is sufficient.
E:Statements (1) and (2) TOGETHER are NOT sufficient.
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正确答案：
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Algebra First-degree equations
Let x be the charge, in dollars, of each additional service. Determine the value of (60)(0.5) + 3x, or equivalently, determine the value of x.
The table below shows the value of x for each of the three possible massages that Jordan had.
From the table it follows that there are two possible values of x, namely x = 7.5 and x = 2.5; NOT sufficient.
The table below shows the value of x for each of the three possible massages that Ryan had.
From the table it follows that there are three possible values of x, namely x = 22.5, x = 15, and x = 7.5; NOT sufficient.
Given (1) and (2), it follows that x = 7.5.
The correct answer is C;both statements together are sufficient.
Let x be the charge, in dollars, of each additional service. Determine the value of (60)(0.5) + 3x, or equivalently, determine the value of x.
The table below shows the value of x for each of the three possible massages that Jordan had.
| Massage | Total charge | x |
| 30-minute | 15 + 3x = 37.50 | 7.50 |
| 60-minute | 30 + 3x = 37.50 | 2.50 |
| 90-minute | 45 + 3x = 37.50 | −2.50 |
From the table it follows that there are two possible values of x, namely x = 7.5 and x = 2.5; NOT sufficient.
The table below shows the value of x for each of the three possible massages that Ryan had.
| Massage | Total charge | x |
| 30-minute | 15 + 2x = 60 | 22.50 |
| 60-minute | 30 + 2x = 60 | 15.00 |
| 90-minute | 45 + 2x = 60 | 7.50 |
From the table it follows that there are three possible values of x, namely x = 22.5, x = 15, and x = 7.5; NOT sufficient.
Given (1) and (2), it follows that x = 7.5.
The correct answer is C;both statements together are sufficient.
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