alleryStart learning →The sum of two numbers is 10. One number is 4 less than the other. Find the numbers.
A4 and 6
B3 and 7
C2 and 8
D5 and 5
Answer & Solution
Correct answer: B. 3 and 7
1. Let n and m be the two numbers, giving the system n + m = 10 and n = m - 4.
2. Substitute m - 4 for n in the first equation: (m minus 4) plus m equals 10.
3. Simplify: 2m minus 4 equals 10, so 2m equals 14, giving m equals 7.
4. Substitute back to find n equals m minus 4, which is 3, so the numbers are 3 and 7.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.4 Solve Applications with Systems of Equations_
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