SOLUTION: Mrs. Reyes bought a television set and a DVD player. After paying a 60% down payment on each item, she paid the rest in 12 monthly installments. After half a year, Mrs. Reyes paid

Question 1172092: Mrs. Reyes bought a television set and a DVD player. After paying a 60% down payment on each item, she paid the rest in 12 monthly installments. After half a year, Mrs. Reyes paid 1/4 more for the balance owed for the television set than the DVD player. If she had already paid P2000 more for television set, what was the total amount she would have to pay in installment each month if she only paid a 55% down payment on each item?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
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.
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