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Algebra Difficulty 2.1 Junior Find the answer

Isaac has written down one integer two times and another integer three times. The sum of the five numbers is 100, and one of the numbers is 28. What is the other number?

Pick one

Solution

Let aa be the number written two times, and bb the number written three times. Then 2a+3b=1002a + 3b = 100. Plugging in a=28a = 28 doesn't yield an integer for bb, so it must be that b=28b = 28, and we get 2a+84=1002a + 84 = 100. Solving for aa, we obtain a=(A)  8a = \boxed{\textbf{(A)}\; 8}.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.