Reggie bought 54 more buttons than Neave and Neave bought 30 buttons more than Billy. The total number of buttons Reggie and Neave bought was 4 times the number of buttons Billy bought.
- How many buttons does Reggie need to give Neave so that they have the same number of buttons?
- How many buttons did all three of them have altogether?
(a)
Since Reggie had 54 buttons more than Neave, Reggie needed to give half of his extra buttons to Neave.
Number of buttons that Reggie needs to give to Neave
= 54 ÷ 2
= 27
(b)
Number of buttons that Billy bought = 1 u
Number of buttons that Neave bought = 1 u + 30
Number of buttons that Reggie bought
= 1 u + 30 + 54
= 1 u + 84
Number of buttons that Neave and Reggie bought
= 1 u + 30 + 1 u + 84
= 2 u + 114
Total number of buttons that Reggie and Neave bought is 4 times the number that Billy bought.
Number of buttons that Neave and Reggie bought = 4 u
4 u = 2 u + 114
4 u - 2 u = 114
2 u = 114
1 u = 114 ÷ 2 = 57
Total number of buttons
= 4 u + 1 u
= 5 u
= 5 x 57
= 285
Answer(s): (a) 27; (b) 285
