a sum of money is divided among asif anwar and sara in the ratio 9 : 8 : 7 after asif gives $25 each to anwar and sara, the ratio becomes 16 : 17 : 15. calculate the amount of money Asif had initially.
Answers
Answer:
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Step-by-step explanation:
Given: Sum of money is divided among Asif Anwar and Sara in the ratio 9:8:7.
The money Asif gives each to Anwar and Sara= $25
After giving the money, a new ratio is 16:17:15.
To find The amount of money Asif had initially
Solution: Let the common ratio of 9:8:7 be x, then the new ratios become 9x, 8x, 7x.
As Asif distribute $25 each to Anwar and Sara,
∴Now, Asif had (9x-50) money and
Anwar had (8x+25) money and Sara had (7x+25) money
Now let the common ratio of 16:17:15 be y, then the new ratios become 16y, 17y, 15y.
The equations will be,
9x-50=16y [for Asif]
⇒9x-16y=50 [Rearranging the sides] (i)
8x+25=17y [for Anwar]
⇒8x-17y=-25 [Rearranging the sides] (ii)
7x+25=15y [for Sara]
⇒7x-15y=-25 [Rearranging the sides] (iii)
Preparing equations(i) and (ii) for simultaneous linear equations, we have
9x-16y=50
⇒(9×7)x-(16×7)y=50×7 [multiplying both sides by 7]
⇒63x-112y=350 (iv)
7x-15y=-25
⇒(7×9)x-(15×9)y=-(25×9) [multiplying both sides by 9]
⇒63x-135y=-225 (v)
Subtracting (v) from (iv), we get
63x-112y=350
-63x+135y=+225 [changing signs of 63x-135y=-225 as it is a rule while we
_____________ are performing subtraction]
0 + 23y=575
⇒y= 575/23
= 25
Now substituting the value y=25 in (i), we get
9x-(16×25)=50
⇒9x-400=50
⇒9x=50+400
⇒x=450/9
⇒x=50
Hence the amount of money Asif had initially is $9x that is $(9×50)=$450.