Question:
Aaron, Bala and Caleb had some savings. Aaron saved 50% as much as the total amount saved by Bala and Caleb. Bala saved 75% as much as the total amount saved by Aaron and Caleb. Aaron saved $7048 more than Caleb. How much did the 3 boys save altogether?
Solution:
![P6 / ACS / 2019 / CA1 – Q04 [1 mark]](https://i0.wp.com/sgprimaths.com/wp-content/uploads/2021/01/P6_ACS_2019_CA1_Q04-Qns.jpg?resize=400%2C260&ssl=1)
![P6 / Catholic High / 2021 / SA2 / Paper 2
– Q04 [2 marks]](https://i0.wp.com/sgprimaths.com/wp-content/uploads/2022/05/P6_SA2_2021_Catholic_High_Paper2_Q04-Qns.jpg?resize=400%2C185&ssl=1)
why does the top model each part has 7 u but the bottom model each part as 9 units
Hi!
That is a good question! Apologies if this was not explained in my solution.
Explanation:
Scenario 1:
A is 50% of (B+C).
This means A = 1u, (B+C) = 2u.
Total = 3u
Scenario 2:
B is 75% of (A+C).
This means B = 3v, (A+C) = 4v.
Total = 7v
The total in Scenario 1 (3u) and Scenario 2 (7v) are actually the same total.
In order to compare them, we need to change these 2 numbers (3 and 7) to be the same.
The lowest common multiple is 3 x 7 = 21p.
Therefore,
Scenario 1:
A = 1u -> 1×7 = 7p
B+C = 2u -> 2×7 = 14p
Total = 21p
Scenario 2:
B = 3v -> 3×3 = 9p
A+C = 4v -> 4×3 = 12p
Total = 21p
Hope this helps to clarify!