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Valrom
30.05.2021 •
Mathematics
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Ответ:
Im sosorry my internet is so poor sorry.
Ответ:
Amount borrowed at 9% = 9,428.57
Amount borrowed at 7% = $18,857.14
Amount borrowed at 10% = $ 21,714.29
Step-by-step explanation:
Formula for simple interest :
I = PRT,
P= Principal, R =rate , T= time
Let x = amount borrowed at 9%.
y = amount borrowed at 7%.
z = amount borrowed at 10%.
i.e. x+y+z= 50000 (i) [Given : amount invested = 50000]
Interest on x = x (0.09)(1) [as P=x, T=1 year, r= 0.09]
= 0.09x
Similarly
Interest on y = y(0.07)(1) = 0.07y
Interest on z = z(0.1)(1)=0.1z
Total interest = 0.09x+0.07y+0.1z = 4340 (ii)
Also, y=2x [given] (iii)
Put y=2x in (i) and (ii), we get
x+2x+z= 50000 ⇒ 3x+z=50000 (iv)
0.09x+0.07(2x)+0.1z=4340 ⇒ 0.09x+0.14x+0.1z=4340
⇒ 0.23x+0.1z=4340 (v)
Multiply 10 on both sides of (v)
2.3x+z=43400 (vi)
Eliminate (vi) from (v)
0.7x=6600
⇒ x= 9,428.57
From (iii), y= 2(9428.57) =18,857.14
From (vi),
2.3(9428.57)+z=43400
⇒ 21685.71+z=43400
⇒ z= 43400-21685.71
⇒ z=21714.29
Hence, Amount borrowed at 9% = 9,428.57
Amount borrowed at 7% = $18,857.14
Amount borrowed at 10% = $ 21,714.29