SOLUTION: the money that tia borrowed at 1% interest was $500 less than three times the amount she borrowed at 12%. how much did she borrow at each rate if she had to pay a total of $418.16
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Question 643125: the money that tia borrowed at 1% interest was $500 less than three times the amount she borrowed at 12%. how much did she borrow at each rate if she had to pay a total of $418.16 annual interest?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x equal the amount of money borrowed at 1%.
let y equal the amount of money borrowed at 12%.
.01*x + .12*y = 418.16
that's one of the formulas you need to work with.
you are given that the money borrowed at 1% interest is equal to 500 less than 3 times the money borrowed at 12%.
since x is the money borrowed at 1% and y is the money borrowed at 12%, this becomes:
x = 3*y - 500
you now have 2 formulas to work with.
the first one is:
.01*x + .12*y = 418.16
the second one is:
x = 3*y - 500
substitute 3*y - 500 from the second equation for x in the first equation to get:
.01 * (3*y-500) + .12*y = 418.16
simplify by removing parentheses to get:
.01*3*y - .01*500 + .12*y = 418.16
simplify further to get:
.03*y - 5 + .12*y = 418.16
combine like terms to get:
.15*y - 5 = 418.16
add 5 to both sides of the equation to get:
.15*y = 418.16 + 5 which simplifies to:
.15*y = 423.16
divide both sides of the equation by .15 to get:
y = 423.16/.15 which simplifies to:
y = 2821.066667
since x is equal to 3 * y - 500, then:
x = 7963.2
your answer is:
x = 7963.2 and y = 2821.07 rounded to the nearest hundred.
.01 * 7963.2 + .12 * 2821.07 = 418.16
this confirms the solutions are good.
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