Question 1172092
Let's break down this problem step-by-step.

1. Define Variables

Let T be the total price of the television set.
Let D be the total price of the DVD player.
2. Set Up Equations Based on the Given Information

60% Down Payment:
Mrs. Reyes paid 0.6T as a down payment for the TV and 0.6D for the DVD player.
The remaining balance for the TV is 0.4T, and for the DVD player is 0.4D.
12 Monthly Installments:
The monthly installment for the TV is 0.4T / 12, and for the DVD player is 0.4D / 12.
Half a Year (6 Months):
After 6 months, Mrs. Reyes had paid half of the balance: 0.2T for the TV and 0.2D for the DVD player.
1/4 More for TV Balance:
The remaining balance for the TV after 6 months was 1/4 more than the remaining balance for the DVD player:
0.2T = 0.2D + (1/4)(0.2D)
0.2T = 0.2D + 0.05D
0.2T = 0.25D
T = 1.25D
P2000 More for TV:
Mrs. Reyes had already paid P2000 more for the TV:
0.6T + 0.2T = 0.6D + 0.2D + 2000
0.8T = 0.8D + 2000
3. Solve for T and D

Substitute T = 1.25D into the second equation:
0.8(1.25D) = 0.8D + 2000
D = 0.8D + 2000
0.2D = 2000
D = 10000
Substitute D back into T = 1.25D:
T = 1.25(10000)
T = 12500
4. Calculate Monthly Installments with 55% Down Payment

55% Down Payment:
New balance for the TV: 0.45T = 0.45(12500) = 5625
New balance for the DVD player: 0.45D = 0.45(10000) = 4500
Total New Balance:
Total balance = 5625 + 4500 = 10125
Monthly Installment:
Monthly installment = 10125 / 12 = 843.75
Answer

The total amount she would have to pay in installments each month if she only paid a 55% down payment on each item is P843.75.