algebra

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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 -

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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