Hi,
I really appreciate someone can help for this question. Thank you.
Huda and Peiqi went shopping with a sum of money. Huda had $30 more than Peiqi. Huda spent thrice as much money as Peiqi. The amount Peiqi had left was $18 more than what she had spent. Peiqi had twice as much money left as Huda. How much money did Huda have at first?
Khong Pek Mao
This is a Matrix question.
We shall start with the cross ratio.
|
|
Spend | save | Total |
| Huda | 6u | 1u + 9 | 7u + 9 |
| Peiqi | 2u | 2u + 18 | 4u + 18 |
7u + 9 = 4u + 18 + 30
7u – 4u = 48 – 9
3u = 39
1u = 13
7u = 7 × 13 = 91
91 + 9 = 100
Alternatively,
Huda :
money at first ——- 1u + 30
spending ——- 3p
Peiqi :
money at first ——- 1u
spending ——- 1p
1u – 1p = 1p + 18
1p ——- (1u – 18)/2
(1u + 30 – 3p) x 2 = 2u + 60 – 6p
2u + 60 – 6p = 1u – 1p
1u ——- 5p – 60 = 5 x [(1u – 18)/2] – 60
2u ——- 5u – 90 – 120
1u ——- (90 + 120)/(5 – 2) = 70
1u + 30 = 70 + 30 = 100
Ans : $100.
