If Jade gives Mark $34, the amount of money she has will be 40% of his. If Mark gives Jade $35, he will have the same amount of money as her. How much money did each of them have?
(a) Mark
(b) Jade
|
Case 1 |
Case 2 |
|
Mark |
Jade |
Mark |
Jade |
Before |
5 u - 34 |
2 u + 34 |
3.5 u + 35 |
3.5 u - 35 |
Change |
+ 34 |
- 34 |
- 35 |
+ 35 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Jade gives to Mark, there is an internal transfer of money from Jade to Mark. The total amount that both have remains the same.
In Case 2, when Mark gives to Jade, there is an internal transfer of money from Mark to Jade. The total amount that both have remains the same.
The total amount that both have in Case 1 and Case 2 are the same.
Total amount that Jade and Mark have
= 5 u + 2 u
= 7 u
Amount that Jade and Mark each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Mark has at first is the same in Case 1 and Case 2.
5 u - 34 = 3.5 u + 35
5 u - 3.5 u = 35 + 34
1.5 u = 69
1 u = 69 ÷ 1.5 = 46
Amount that Mark has
= 5 u - 34
= 5 x 46 - 34
= 230 - 34
= $196
(b)
Amount that Jade has
= 2 u + 34
= 2 x 46 + 34
= 92 + 34
= $126
Answer(s): (a) $196; (b) $126