Jack bought 34 more buttons than Ethan and Ethan bought 28 buttons more than Yoko. The total number of buttons Jack and Ethan bought was 5 times the number of buttons Yoko bought.
- How many buttons does Jack need to give Ethan so that they have the same number of buttons?
- How many buttons did all three of them have altogether?
Jack |
Ethan |
Yoko |
1 u + 28 + 34 |
1 u + 28 |
1 u |
5 u |
1 u |
(a)
Number of buttons that Jack needs to give Ethan so that they have same number of buttons
= 34 ÷ 2
= 17
(b)
Total number of buttons that Jack and Ethan had
= 1 u + 28 + 34 + 1 u + 28
= 1 u + 1 u + 28 + 34 + 28
= 2 u + 90
5 u = 2 u + 90
5 u - 2 u = 90
3 u = 90
1 u = 90 ÷ 3 = 30
Total number of buttons that all three of them had
= 5 u + 1 u
= 6 u
= 6 x 30
= 180
Answer(s): (a) 17; (b) 180