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The sum of two positive numbers is 45 and their difference is 19. What are the numbers?
25, 20
32, 13
31, 15
30, 15
32, 13
Let the numbers be x and y. Then x = (Sum + Difference) / 2 and y = (Sum - Difference) / 2. Here, x = (45+19)/2 = 64/2 = 32, and y = (45-19)/2 = 26/2 = 13.
Sum of two positive numbers is 45, and their difference is 19.
x+y=45 and xтИТy=19
Let the numbers be x and y. Then x = (Sum + Difference) / 2 and y = (Sum - Difference) / 2. Here, x = (45+19)/2 = 64/2 = 32, and y = (45-19)/2 = 26/2 = 13.
Many students subtract the difference from the sum instead of adding, or forget to divide by 2 after adding/subtracting.
Set up equations
Let the two positive numbers be x and y. Based on the problem, we have two linear equations: x+y=45 and xтИТy=19.
x+y=45,xтИТy=19
Add the equations
To solve for x, add both equations together to eliminate y: (x+y)+(xтИТy)=45+19.
2x=64
Solve for x
Divide by 2 to find the first number: x=64/2.
x=32
Solve for y
Substitute x=32 back into the first equation: 32+y=45. Subtract 32 from 45 to find y.
y=45тИТ32=13
B is correct because solving the system of equations x+y=45 and xтИТy=19 yields x=32 and y=13.
This type of system of linear equations is foundational for competitive exams; always check if the sum/difference matches the given values if you are short on time.
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