Asked by Joel
Select the set of equations that represents the following situation: Mary invested one amount at 7% simple interest, and a second amount at 5% interest, earning $29.80 in one year. If she had switched the amounts, she would have earned $35.00. What were the two amounts?
Answers
Answered by
Henry
Invested $X @ 7%.
Invested $Y @ 5%.
Eq1: 0.07X + 0.05Y = $29.80.
Eq2: 0.05X + 0.07Y=35(Amountswitched).
Multiply both Eqs by 100:
7X + 5Y = 2980
5X + 7Y = 3500
Multiply 1st Eq by -5 and 2nd Eq by7:
-35X -25Y = -14900
35X + 49Y = 24500
Add the 2 Eqs and get:
24Y = 9600,
Y = $400.
Substitute 400 for Y in Eq2:
0.05X + 0.07*400 = 35,
0.05X + 28 = 35,
0.05X = 35 - 28 = 7,
X = 7 / 0.05 = $140.
Invested $Y @ 5%.
Eq1: 0.07X + 0.05Y = $29.80.
Eq2: 0.05X + 0.07Y=35(Amountswitched).
Multiply both Eqs by 100:
7X + 5Y = 2980
5X + 7Y = 3500
Multiply 1st Eq by -5 and 2nd Eq by7:
-35X -25Y = -14900
35X + 49Y = 24500
Add the 2 Eqs and get:
24Y = 9600,
Y = $400.
Substitute 400 for Y in Eq2:
0.05X + 0.07*400 = 35,
0.05X + 28 = 35,
0.05X = 35 - 28 = 7,
X = 7 / 0.05 = $140.
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.