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2010 AMC 12B Problem 5

Problem 5 of 25EasierAlgebraArithmetic

Lucky Larry’s teacher asked him to substitute numbers for a,a, b,b, c,c, d,d, and ee in the expression a−(b−(c−(d+e)))a-(b-(c-(d+e))) and evaluate the result. Larry ignored the parentheses but added and subtracted correctly and obtained the correct result by coincidence. The numbers Larry substituted for a,a, b,b, c,c, and dd were 1,1, 2,2, 3,3, and 4,4, respectively. What number did Larry substitute for e?e?

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Solution

The correct value is a−(b−(c−(d+e)))=a-(b-(c-(d+e)))= a−b+c−d−e.a-b+c-d-e. With a,b,c,d=1,2,3,4,a, b, c, d=1, 2, 3, 4, this equals 1−2+3−4−e=−2−e.1-2+3-4-e=-2-e. Larry dropped the parentheses and computed 1−2−3−4+e=−8+e.1-2-3-4+e=-8+e. Setting −2−e=−8+e-2-e=-8+e gives 2e=6,2e=6, so e=3.e=3. Thus, the correct answer is D.
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Tagged: order of operations · linear equation

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