In order to complete a reading assignment on time, Terry planned to read 90 pages per day.However,she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all Terry have to complete the assignment on time?
A.15
B.16
C.25
D.40
E.46
This is a weighted average/mixture problem.
First set of days: Average number of pages per day = 75.
Last 6 days: Average number of pages per day = 690/6 = 115.
Mixture of the two sets of days: Average number of pages per day = 90.
Let F = the first set of days and L = the last 6 days.
To determine the ratio of F to L in the mixture, use ALLIGATION:
Step 1: Plot the 3 averages on a number line, with the averages for the two ingredients on the ends and the mixture average in the middle.
F 75-----------------90----------------115 L
Step 2: Calculate the distances between the averages.
F 75--------
15-------90--------
25------115 L
Step 3: Determine the ratio in the mixture.
The required ratio of F to L is the RECIPROCAL of the distances in red.
F:L = 25:15 = 5:3.
Since the actual value of L is 6 days, and F:L = 5:3 = 10:6, F = 10 and L = 6.
Thus, the total number of days = F+L = 10+6 = 16.
The correct answer is
B.
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