Devide 5783 in a, b and c such that if 28, 37 and 18 is substracted respactively from each they are in the ratio 4, 6 and 9. Find value of a.

Question

Algebra question having three variables.

Answer 1

a+b+c=5783; a-28: b-37: c-18=4:6:9. The ratios tell you that the whole is represented by 4+6+9=19 parts, so the fractions are 4/19, 6/19, 9/19. 28+37+18=83, so subtract 83 from 5783=5700. 4/19*5700=1200; 6/19*5700=1800; 9/19*5700=2700. The amounts are 1228, 1837 and 2718 and a is 1228.