Tina and Gem have some shortbreads each. If Tina gives Gem 32 shortbreads, Tina will have
78 as many shortbreads as Gem. If Tina gives Gem 9 shortbreads, they will have an equal number of shortbreads. How many shortbreads does Gem have at first?
|
Case 1 |
Case 2 |
|
Tina |
Gem |
Tina |
Gem |
Before |
7 u + 32 |
8 u - 32 |
7.5 u + 9 |
7.5 u - 9 |
Change |
- 32 |
+ 32 |
- 9 |
+ 9 |
After |
7 u |
8 u |
7.5 u |
7.5 u |
Total number of shortbreads that Tina and Gem have
= 7 u + 8 u
= 15 u
Number of shortbreads that Tina and Gem each has in the end is the same.
Number of shortbreads that Tina and Gem each has in the end in Case 2
= 15 u ÷ 2
= 7.5 u
Number of shortbreads that Tina had at first is the same in Case 1 and Case 2.
7.5 u + 9 = 7 u + 32
7.5 u - 7 u = 32 - 9
0.5 u = 23
1 u = 23 ÷ 0.5 = 46
Number of shortbreads that Gem has
= 8 u - 32
= 8 x 46 - 32
= 368 - 32
= 336
Answer(s): 336