Determine the value of ‘A’?

Solution

ATQ, we can say that Ratio of the investments of Alex and Curry with respect to the time ⇒ (3a-3000)x9+(3a-3000+0.5a)x15 : (2a+2000)x9+(2a+2000-0.25a)x15 = 94 : 67 (3a-3000)x3+(3a-3000+0.5a)x5 : (2a+2000)x3+(2a+2000-0.25a)x5 = 94 : 67 (3a-3000)x3+(3.5a-3000)x5 : (2a+2000)x3+(1.75a+2000)x5 = 94 : 67 (9a-9000)+(17.5a-15000) : (6a+6000)+(8.75a+10000) = 94 : 67 (26.5a-24000) : (14.75a+16000) = 94 : 67 1775.5a −1608000 = 1386.5a + 1504000 1775.5a −1386.5a = 1608000+1504000 389a = 3112000 a = 8000 Ratio of the investments of Alex, Ben and Curry with respect to the time ⇒ (3a-3000)x9+(3a-3000+0.5a)x15 : (2a-1000)x9 : (2a+2000)x9+(2a+2000-0.25a)x15 Put the values of ‘a’ in the above equation. ⇒ (3x8000-3000)x9+(3x8000-3000+0.5x8000)x15 : (2x8000-1000)x9 : (2x8000+2000)x9+(2x8000+2000-0.25x8000)x15 ⇒ (24000-3000)x3+(24000-3000+4000)x5 : (16000-1000)x3 : (16000+2000)x3+(16000+2000-2000)x5 ⇒ (21000)x3+(25000)x5 : (15000)x3 : (18000)x3+(16000)x5 ⇒ (63000+125000) : 45000 : (54000+80000) ⇒ 188000 : 45000 : 134000 ⇒ 188 : 45 : 134 Ratio of the investments of Alex and Curry with respect to the time ⇒ (3a-3000)x9+(3a-3000+0.5a)x15 : (2a+2000)x9+(2a+2000-0.25a)x15 = 94 : 67 (3a-3000)x3+(3a-3000+0.5a)x5 : (2a+2000)x3+(2a+2000-0.25a)x5 = 94 : 67 (3a-3000)x3+(3.5a-3000)x5 : (2a+2000)x3+(1.75a+2000)x5 = 94 : 67 (9a-9000)+(17.5a-15000) : (6a+6000)+(8.75a+10000) = 94 : 67 (26.5a-24000) : (14.75a+16000) = 94 : 67 1775.5a −1608000 = 1386.5a + 1504000 1775.5a −1386.5a = 1608000+1504000 389a = 3112000 a = 8000