Aaron had 3/4 as many badges as Ben. Ben has 2/5 as many badges as Calvin. Aaron has 8 badges fewer than Ben. How many more badges does Calvin have than Ben?
+9673 Let a be the number of badges Aaron has, b be the number of badges Ben has, and c be the number of badge Calvin has.
Then, \(\begin{cases} a &=& \dfrac34 b\\ b &=& \dfrac25 c\\ a &=& b - 8 \end{cases}\)
Plugging in the first equation into the third equation gives \(\dfrac34b = b - 8\). Solving gives b = 32.
Can you take it from here? You can calculate the value of c and calculate c - b to be the answer.
+237 Aaron : Ben
3 : 4
Ben : Calvin
2 : 5
4 : 10
Aaron : Ben : Calvin
3 : 4 : 10
6 : 8 : 20
Calvin has 2 * x badges
Ben has 8x badges
Aaron has 6x badges
from question,
Aaron's badges + 8 = Ben's badges
6x + 8 = 8x
x = 4
20x - 8x = 12x
12 * 4 = 48
48 more badges Calvin have than Ben.
