Oliver and Marie open bank accounts at the same time. Oliver deposits $300 initially and adds $10
per week. Marie deposits $200 initially and adds
$20 per week. After how many weeks of making
additional deposits will Oliver and Marie have the
same amount of money in the account?
A. 10 weeks
C. 40 weeks
B. 2 weeks
D. 30 weeks

A. 10 weeks

Step-by-step explanation:

Oliver  Marie

Starting300  200

week 1310  220

week 2320  240

week 3330  260

week 4340  280

week 5350  300

week 6360  320

week 7370  340

week 8380  360

week 9390  380

week 10400  400

9514 1404 393

  A. 10 weeks

Step-by-step explanation:

Marie's balance is initially $100 less, but she deposits $10 more per week than Oliver does. It will take her 100/10 = 10 weeks to catch up to Oliver's balance.

Oliver and Marie will have the same balance after 10 weeks.

__

Oliver's balance at that time will be 300 +10×10 = 400.

Marie's balance at that time will be 200 +10×20 = 400. (the same)

Let's define the variables:

L = length of the room

B = breadth of the room

H = height of the room.

We know that:

L = 2*B

L = 3*H

Remember that the area of a rectangle of length L and breadth B is:

A = L*B

Then the area of the floor of the room is:

A = L*B

and L = 2*B, if we replace that, we get:

A = (2*B)*B

A = 2*B^2

Now, we know that the cost of carpeting the floor is $80 per m^2

And the total cost was $9000

Then the number of square meters in the floor (thus, the area of the floor) is:

A = ($9000)/($80)  m^2

A = 112.5 m^2

With this, we can find the value of B.

A = 112.5 m^2 = 2*B^2

B = √( 112.5/2) m = 7.5 m

Then the length is:

L = 2*B = 2*7.5m = 15m

And the height is:

L = 3*H

H = L/3 = 15m/3 = 5m

Now that we know all the dimensions of the room, we need to find the area of the four walls, and the area of the ceiling (which is equal to the area of the floor 112.5 m^2)

Now, we will have two walls with an area of:

area = breadth*height = B*H = (7.5m)*(5m) = 37.5m^2

And two walls with an area of:

area = length*height = L*H = 75m^2

Then the total area of the four walls plus the ceiling is:

A' = 2*(37.5m^2) + 2*( 75m^2) + 112.5 m^2

A' = 337.5 m^2

And we know that for each m^2, the cost of plastering is $35

Then for 337.5 m^2, the cost will be 337.5 times $35

Cost = (337.5)*$35 = $11,812.50