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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?

 Jun 16, 2022
 #1
avatar+9458 
0

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.

 Jun 16, 2022
 #2
avatar+229 
+1

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.

 Jun 16, 2022

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