SOLUTION: Mrs. Diez has savings account in two banks. The combined amount of these saving is at least 150,000. One bank gave an interest of 4% while the other bank gives 6%. In a year, M

Question 1188280: Mrs. Diez has savings account in two banks. The combined amount of these saving is at least 150,000.
One bank gave an interest of 4% while the other bank gives 6%.
In a year, Mrs. Diez receives at most 12,000.
1. What mathematical statements represent the given situation?
2. Draw the graphs of the mathematical statments.
3. How will you detemine the amount of savings in each bank account?
4. Give one possible amount of savings in both accounts.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Mrs. Diez has savings account in two banks. The combined amount of these saving is at least 150,000.
One bank gave an interest of 4% while the other bank gives 6%.
In a year, Mrs. Diez receives at most 12,000.
1. What mathematical statements represent the given situation?
x = amount invested at 4%.
y = amount invesed at 6%.
x + y >= 150000
.04x + .06y <= 12000
2. Draw the graphs of the mathematical statements.

3. How will you determine the amount of savings in each bank account?
the graph shows the opposite of the constraint inequalities.
x + y >= 150,000 is graphed as x + y <= 150,000.
.04x + .06y <= 12000 is graphed as .04x + .06y >= 12000.
x >= 0 is graphed as x <= 0.
y >= 0 is graphed as y <= 0.
the area of the graph that is NOT SHADED is the region of fesibility.
all coordinate points within this region are valid and satisfy all the constraints.
4. Give one possible amount of savings in both accounts.
one coordinate point would be (300,000,0).
this means all the investments yield 4% interest.
if the interest was 12,000, then the amount invested had to be 12,000 / .04 = 300,000.
another point within the feasible region would be (100,000,100,000).
the amount invested would be 200,000 which is greater than 150,000.
the interest would be .04 * 100,000 + .06 * 100,000 = 10,000 which is less than 12,000.
a point outside the feasible region would be (150,000,200,000).
the amount invested is equal to 350,000 which is greater than 150,000.
the interest would be .04 * 150,000 + .06 * 200,000 = 18,000 which is NOT less than 12,000.

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