AMC12 2015 B

AMC12 2015 B · Q3

AMC12 2015 B · Q3. It mainly tests Linear equations.

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?

Isaac写下了一个整数两次，另一个整数三次。这五个数的和是100，其中一个数是28。另一个数是多少？

(A) 8 8

(B) 11 11

(D) 15 15

(E) 18 18

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): Let $x$ be the integer Isaac wrote two times, and let $y$ be the integer Isaac wrote three times. Then $2x + 3y = 100$. If $x = 28$, then $3y = 100 - 2 \cdot 28 = 44$, and $y$ cannot be an integer. Therefore $y = 28$ and $2x = 100 - 3 \cdot 28 = 16$, so $x = 8$.

答案（A）：设 $x$ 为 Isaac 写了两次的整数，设 $y$ 为 Isaac 写了三次的整数。则 $2x + 3y = 100$。若 $x = 28$，则 $3y = 100 - 2 \cdot 28 = 44$，此时 $y$ 不可能是整数。因此 $y = 28$，并且 $2x = 100 - 3 \cdot 28 = 16$，所以 $x = 8$。

Topics

AL.001 Linear equations