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Nadia has 3 times as many stamps as Evan and 50 more stamps than Kate. They have 972 stamps altogether. How many more stamps does Kate have than Evan

Respuesta :

nadia has 438stamps
evan has 146 stamps 
kate has 388
answer is 242

Let Nadia has [tex] N [/tex] stamps.

Let Evan has [tex] E [/tex] stamps.

Let Kate has [tex] K [/tex] stamps.

From the given information,

[tex] N=3E\\
N=K+50\\
N+E+K=972\\
[/tex]

Solve the above equations together.

[tex] 3E+E+3E-50=972\\
7E=972+50\\
7E=1022\\
E=146 [/tex]

[tex] K=3E-50=3*146-50=388 [/tex].

So,

[tex] K-E=388-146=242 [/tex].

Hence, Kate has 242 cards more than Evan.

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