The sum of two numbers is 24. Three times the smaller numbers is 3 less than twice the larger number. Find the numbers.

9, 15

Step-by-step explanation:

x = smaller number

y = larger number

system of equations:

x + y = 24

3x = 2y - 3

substitution method:

x = 24 - y

3(24 - y) = 2y - 3

72 - 3y = 2y - 3

72 = 5y - 3

75 = 5y

y = 15

x + 15 = 24

x = 9

geometry: triangles

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answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584