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Algebra Difficulty 2.7 Junior Find the answer

In the subtraction shown, K,L,MK, L, M, and NN are digits. What is the value of K+L+M+NK+L+M+N?

A number or a short expression. Spacing and $ signs are ignored.

Solution

We work from right to left as we would if doing this calculation by hand. In the units column, we have L1L-1 giving 1. Thus, L=2L=2. (There is no borrowing required.) In the tens column, we have 3N3-N giving 5. Since 5 is larger than 3, we must borrow from the hundreds column. Thus, 13N13-N gives 5, which means N=8N=8. In the hundreds column, we have (K1)4(K-1)-4 giving 4, which means K=9K=9. In the thousands column, we have 5 (with nothing borrowed) minus MM giving 4. Thus, 5M=45-M=4 or M=1M=1. Finally, K+L+M+N=9+2+1+8=20K+L+M+N=9+2+1+8=20.

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