Applications of systems

Question

You split $1500 between two savings accounts. One pays %4 interest, and the other pays %5. After one year you have earned $69.50 in interest. How much was the %4 account?

Answer 1

Alexia, it doesn't specify how the $1500 was split so that is what you are trying to solve. Use the following equations (5% = 0.05; 4% = 0.04):

A + B = 1500

0.05A + 0.04B = 69.50

STEP 1: Multiply the second equation by -20 on both sides which will give you a -A value

A + B = 1500

(-20)0.05A + 0.04B = 69.50 (-20)

A + B = 1500

-A - 0.8B = -1390

STEP 2: Add top equation to bottom equation removing 'A'

A + B = 1500

-A - 0.8B = -1390

0.2B = 110

STEP 3: Solve for B by dividing 0.2 on both sides

0.2B = 110

0.2

B = 550; You deposited $550 in the 4% savings account.

STEP 4: Plug in 550 for 'B' in the first equation to solve for 'A'

A + B = 1500

A + 550 = 1500

A = 950; You deposited $950 in the 5% savings account.

STEP 5: Verify that A=950 and B=550 works for the second $ equation

0.05A + 0.04B = 69.50

0.05(950) + 0.04(550) = 69.50

47.5 + 22 = 69.50

69.50 = 69.50

The answer is: you deposited $550 in the 4% savings account.

Let me know if you have additional questions.

-TutorB

Answer 2

Hi Alexia, Let x represent the amount of money in the 4% account. Then the 5% account would have (1500 - x) in it.

The equation to solve is:

.04x + .05 * (1500 - x) = 69.50

.04x + 75 - .05x = 69.50

Combine terms:

-.01x = -5.50

x = 550

The 4% account would have $550.

The 5% account would have 1500 - 550, or $950.

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