Posted by **Joel** on Tuesday, February 22, 2011 at 10:36am.

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?

- algebra -
**Henry**, Wednesday, February 23, 2011 at 11:28pm
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.

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