If Zoe gives Bobby $26, the amount of money she has will be 10% of his. If Bobby gives Zoe $190, he will have the same amount of money as her. How much money did each of them have?
(a) Bobby
(b) Zoe
|
Case 1 |
Case 2 |
|
Bobby |
Zoe |
Bobby |
Zoe |
Before |
10 u - 26 |
1 u + 26 |
5.5 u + 190 |
5.5 u - 190 |
Change |
+ 26 |
- 26 |
- 190 |
+ 190 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Zoe gives to Bobby, there is an internal transfer of money from Zoe to Bobby. The total amount that both have remains the same.
In Case 2, when Bobby gives to Zoe, there is an internal transfer of money from Bobby to Zoe. 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 Zoe and Bobby have
= 10 u + 1 u
= 11 u
Amount that Zoe and Bobby each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Bobby has at first is the same in Case 1 and Case 2.
10 u - 26 = 5.5 u + 190
10 u - 5.5 u = 190 + 26
4.5 u = 216
1 u = 216 ÷ 4.5 = 48
Amount that Bobby has
= 10 u - 26
= 10 x 48 - 26
= 480 - 26
= $454
(b)
Amount that Zoe has
= 1 u + 26
= 1 x 48 + 26
= 48 + 26
= $74
Answer(s): (a) $454; (b) $74