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12 Dec 2018, 03:18
Kudos
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Difficulty:
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A company received two shipments of ball bearings. In the first shipment, 1 percent of the ball bearings were defective. In the second shipment, which was twice as large as the first, 4.5 percent of the ball bearings were defective. If the company received a total of 100 defective ball bearings, how many ball bearings were in the first shipment?
A. 990
B. 1,000
C. 2,000
D. 3,000
E. 3,500
A. 990
B. 1,000
C. 2,000
D. 3,000
E. 3,500
12 Dec 2018, 03:22
Kudos
Bookmarks
Bunuel
A company received two shipments of ball bearings. In the first shipment, 1 percent of the ball bearings were defective. In the second shipment, which was twice as large as the first, 4.5 percent of the ball bearings were defective. If the company received a total of 100 defective ball bearings, how many ball bearings were in the first shipment?
A. 990
B. 1,000
C. 2,000
D. 3,000
E. 3,500
A. 990
B. 1,000
C. 2,000
D. 3,000
E. 3,500
given B=2A
and 0.01A+0.045B=100
or say 0.01A+0.045 * 2A= 100
solve for A = 1000 IMO B
26 Mar 2020, 06:53
Kudos
Bookmarks
Bunuel
A company received two shipments of ball bearings. In the first shipment, 1 percent of the ball bearings were defective. In the second shipment, which was twice as large as the first, 4.5 percent of the ball bearings were defective. If the company received a total of 100 defective ball bearings, how many ball bearings were in the first shipment?
A. 990
B. 1,000
C. 2,000
D. 3,000
E. 3,500
A. 990
B. 1,000
C. 2,000
D. 3,000
E. 3,500
Let x = the total number of ball bearings in the first shipment
The second shipment, which was twice as large as the first
So, 2x = the total number of ball bearings in the second shipment
In the first shipment, 1 percent of the ball bearings were defective
So, 1% of x = total number of DEFECTIVE ball bearings in the first shipment
In other words, 0.01x = total number of DEFECTIVE ball bearings in the first shipment
In the second shipment, 4.5 percent of the ball bearings were defective.
So, (0.045)(2x) = total number of DEFECTIVE ball bearings in the second shipment
In other words, 0.09x = total number of DEFECTIVE ball bearings in the second shipment
If the company received a total of 100 DEFECTIVE ball bearings, how many ball bearings were in the first shipment?
We can write: 0.01x + 0.09x = 100
Simplify: 0.1x = 100
Solve: x = 100/0.1 = 1000
Answer: B
Cheers,
Brent
