Ella, Ian and Janice shared the cost of a present. Ella paid twice the amount Janice paid, while Janice paid ₱160 more than Ian. Ian paid ₱240 for his share of the present.(a) Write the ratio of Ella’s share to Ian’s share to Janice’s share for the cost of the present. : : (b) Find the total cost of the present. ₱
Question
Ella, Ian and Janice shared the cost of a present. Ella paid twice the amount Janice paid, while Janice paid ₱160 more than Ian. Ian paid ₱240 for his share of the present.(a) Write the ratio of Ella’s share to Ian’s share to Janice’s share for the cost of the present. : : (b) Find the total cost of the present. ₱
Solution
(a) Let's denote Ella's share as E, Ian's share as I, and Janice's share as J.
From the problem, we know that:
- E = 2J (Ella paid twice the amount Janice paid)
- J = I + ₱160 (Janice paid ₱160 more than Ian)
- I = ₱240 (Ian paid ₱240 for his share of the present)
Substituting the second and third equations into the first, we get: E = 2(I + ₱160) = 2(₱240 + ₱160) = ₱800
So, the ratio of Ella’s share to Ian’s share to Janice’s share for the cost of the present is 800 : 240 : 400.
(b) To find the total cost of the present, we add up all their shares: Total cost = E + I + J = ₱800 + ₱240 + ₱400 = ₱1440.
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