Question

Eighty members of a bike club were asked whether they like touring bikes and whether they like mountain bikes. A total of 70 like touring bikes, 47 like mountain bikes, and 5 do not like either.
A 4-column table with 3 rows. The first column has no label with entries likes mountain bikes, does not like mountain bikes, total. The second column is labeled liking touring bikes with entries a, c, 70. The third column is labeled does not like touring bikes with entries b, 5, e. The fourth column is labeled total with entries 47, d, 80.

What are the correct values of a, b, c, d, and e?

a = 42, b = 28, c = 33, d = 5, e = 10
a = 42, b = 5, c = 28, d = 33, e = 10
a = 5, b = 42, c = 28, d = 10, e = 33
a = 5, b = 10, c = 28, d = 33, e = 42

Answer 1

Answer: Choice B

a = 42, b = 5, c = 28, d = 33, e = 10

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Explanation:

Refer to the diagram below. We have a table of values in which some values (if not most) are unknown. We have variables as placeholders until we can figure out which numbers replace them.

Along the bottom row, we see that 70+e = 80, which solves to e = 10. I subtracted 70 from both sides.

That must mean the answer is between choice A or choice B.

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Since e = 10, and b+5 = e (third column), we can replace the 'e' with 10 to get the equation b+5 = 10. That solves to b = 5. This rules out choice A.

The final answer is choice B

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If you want to keep going to find a, c and d, then let's solve a+b = 47 which is the same as a+5 = 47 after replacing letter b with 5.

a+5 = 47 solves to a = 42 after subtracting both sides by 5.

Then along the first column, we see that a+c = 70 which is the same as 42+c = 70. Isolating c gets us c = 28

Lastly, c+5 = d is shown along the second row. Plug in c = 28 to find that d = c+5 = 28+5 = 33

So overall we have:

a = 42, b = 5, c = 28, d = 33, e = 10