Math/ (bank question) help?

Question

John has a credit card from Bagel Bank and another from Arctic Bank. He has a total of $1,190 charged on his credit cards. Bagel Bank charges 15% simple interest per year and Arctic Bank charges 16% per year. The yearly interest charge John needs to pay is $183.90. How much money does John owe Bagel Bank before interest charges?

Answer 1

Borrowed - $1,190
Bagel(B) Bank @ 15%
Arctic (A) Bank @ 16%
Interest charged - $183∙90

B + A = 1190
0∙15B + 0∙16A = 183∙90 (÷ 0∙15)
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B + A = 1190 ( -)
B + 1∙066...A = 1226
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0∙066..A = 36
A = 540∙0
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B + A = 1190
B = 1190 - A
B = 650


(B) $650 x 15% = $650 x 97∙5 = $747∙50
(A) $540 x 16% = $540 x 86∙4 = $626∙40
(B) + (A) = $747∙50 + $626∙40 = $ 1373∙90

Answer ; $650

Answer 2

He owes Bagel Bank 650.
This is a simulataneous equation problem. If X is the amount he owes Bagel, and Y the amount he owes Arctic... then

X+ Y = 1190 and
15x + 16y = 18390 [ both sides multiplied by 100]

X = 1190 - Y
substituting this ...
15(1190 - Y) + 16 Y = 18390
17850 - 15Y + 16Y = 18390
17850 + Y = 18390
Y = 18390 - 17850
Y = 540

Back to the substitution
X = 1190 - Y
x = 1190 - 540
x = 650