I desperately need help with this question. Help would be greatly appreciated

Question

Formulate a system of equations for the situation below and solve.

Michael Perez deposited a total of $2000 with two savings institutions. Bank A pays interest at the rate of 5%/year, whereas Bank B pays interest at the rate of 8%/year. If Michael earned a total of $112 in interest during a single year, how much did he deposit in each institution?

Bank A	$
Bank B	$

Answer 1

112/2000 = 0.056 = 5.6%

which is within 0.6 of 5 and 2.4 of 8

he invested 2.4/.6 = 4 times as much at 5% as at 8%

that's 80% at 5% and 20% at 8%

80% of $2,000 = $1600

20% at $2,000 = $400

or the way you probably want to solve this is:

.08(x) + .05(2000-x) = 112

.08x -.05x = 112 - 100

.03x = 12

x = 12/.03 = 400 at 8%

5%A + 8%B = 112

A+B = 2000

.05A + .08B = 112

A + B = 2000

is probably the system of equations you want.

solve the 2nd equation for B, then substitute that result into the 1st equation, then solve for A =1600, then B=2000-1600=400

.05(1600) + .08(400)

= 80 + 32

= 112

2000-x = 1600 at 5%

Answer 2

Formulate a system of equations for the situation below and solve.

Michael Perez deposited a total of $2000 with two savings institutions. Bank A pays interest at the rate of 5%/year, whereas Bank B pays interest at the rate of 8%/year. If Michael earned a total of $112 in interest during a single year, how much did he deposit in each institution?

Bank A: $x ??

Bank B: $y ??

Detailed Solution:

============

Let: Bank A = x $ and Bank B = y $; Total = $2000

Bank A pays = (5%)(x) = 0.05x and Bank A pays = (8%)(y) = 0.08y; Total = $112

x + y = 2000 ==> y = 2000 - x ==> (1)

0.05x + 0.08y = 112 ==> (2)

Substitute eqn (1) into eqn (2)

0.05x + 0.08y = 112 ==> 0.05x + 0.08(2000 - x) = 112 ==> 0.05x + 160 - 0.08x = 112 ==> 160 - 0.03x = 112 ==> 0.03x = 160 - 112 ==> 0.03x = 48 ==> x = 1600

Substitute x = 1600 into eqn (1)

y = 2000 - x ==> y = 2000 - 1600 ==> y = 400

Final Solution: (x, y) = (1600, 400)

Bank A: x = $1,600

Bank B: y = $400

Check The Solution: (x, y) = (1600, 400)

=============================

x + y = 2000 ==> (1): 1600 + 400 = 2000 ==> 2000 = 2000

0.05x + 0.08y = 112 ==> 0.05(1600) + 0.08(400) = 112 ==> 80 + 32 = 112 ==> 112 = 112