Asked by Anonymous
Mary invested one amount at 5% simple interest, and a second amount at 4% interest, earning $21.32 in one year. If she had switched the amounts, she would have earned $25.84. What were the two amounts?
Answers
Answered by
Henry
$X @ 5%.
$Y @ 4%.
Eq1: 0.05x + 0.04y = 21.32
Eq2: 0.04x + 0.05y = 25.84.
Multiply Eq1 by 400 and Eq2 by -500:
Eq1: +20x + 16y = 8528.
Eq2: -20x - 25y = -12920.
Add the Eqs:
-9y = -4392
Y = $488
In Eq1, substitute 488 for Y:
0.05x + 0.04*488 = 21.32
0.05x + 19.52 = 21.32
0.05x = 21.32 - 19.52 = 1.8
X = 1.8 / 0.05 = $36.
$Y @ 4%.
Eq1: 0.05x + 0.04y = 21.32
Eq2: 0.04x + 0.05y = 25.84.
Multiply Eq1 by 400 and Eq2 by -500:
Eq1: +20x + 16y = 8528.
Eq2: -20x - 25y = -12920.
Add the Eqs:
-9y = -4392
Y = $488
In Eq1, substitute 488 for Y:
0.05x + 0.04*488 = 21.32
0.05x + 19.52 = 21.32
0.05x = 21.32 - 19.52 = 1.8
X = 1.8 / 0.05 = $36.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.