James B. answered • 07/26/16

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Simple Interest Formula

I = Prt

where I = Interested earned

P = principal mount invested

r = interest rate

r - time (in years) ... for this scenario, t = 1

Since we are investing 2 different amounts,

Let x = amount invested at 6.5%

Let y = amount invested at 8 %

The total amount invested is $175,000

x + y = 175,000 (Equation 1)

.065x + .08y = 12,000 (Equation 2)

Using substitution method, solving for y in equation 1, then substituting that into eauation 2 and solving for x,

y = 175,000 - x

.065x + .08y = 12,000

.065x + .08(175,000 - x) = 12,000

.065x + 14,000 - .08x = 12,000

-.015x. = 12,000 - 14,000

-.015x = -2000

x = -2000/(-0.015)

x = 133,333.33

Since 175.000 - 133,000.33 = 41,666.67

$133,333.33 is invested at 6.5 %

$ 41,666.66 is invested at 8 %

CHECK:

6.5% of 133,333.55 = .065(133,333.33) = $8,666.67

8% of 41,666.66 = .08(8666.67) = $3,333.33

TOTAL =$12,000