Clifford has 30 stamps. The total value of all his stamps is $12. Find the number of 50¢ and 20¢ stamps Clifford has.

20 50 cent stamps

 

10 20 cent stamps

I will write everything in cents because I hate decimals more than anything :)).

 

Let $a$ denote the number of $50$ cent stamps he has, and let $b$ denote the number of $20$ cent stamps he has.

 

We have two equations: $a+b=30$ and $50a+20b=1200$.

 

Solving the first equation and substituting:

 

$a=30-b$

$50(30-b)+20b=1200$

$1500-50b+20b=1200$

$-30b=-300$

$30b=300$

$b=10$.

 

Now, we have $a+b=30$, so $a+10=30$, $a=20$.

 

So Clifford has $\boxed{20}$ 50 cent stamps and $\boxed{10}$ 20 cent stamps.

 

A simple check by multiplying them out:

 

$20*50+10*20=1200$

$1000+200=1200$

$1200=1200$(it works!)