Given:
A : B = 7 : 8
B : C = 9 : 10
C : D = 11 : 12
B = 1584
To find:
A + B + C + D
Solution:
Converting ratios into fraction, we will get these 3 equations
[tex]A/B= 7/8 \\B/C = 9/10\\C/D = 11/12[/tex]
Put the value of B and solve for A in the first equation.
[tex]A/1584= 7/8\\[/tex]
Multiply both sides by 8
[tex]8A/1584=7\\A/198=7\\[/tex]
Multiply both sides by 198
[tex]A= 1386[/tex]
Now put the value of B in 2nd equation and solve for C
[tex]1584/C =9/10[/tex]
Multiply both sides by 10C
[tex]15840=9C\\C=15840/9\\C=1760[/tex]
Put the value of C in 3rd equation and solve for D
[tex]1760/D=11/12[/tex]
Multiply both sides by 12D
[tex]21120=11D\\D=21120/11\\D=1920\\[/tex]
Now that we have the value of A, B, C, and D add them up to get the answer.
[tex]1386+1584+1760+1920\\=6650[/tex]
Therefore, A + B + C + D = 6650