Microeconomics problem on choosing an equivalent bundle

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Paul's utility function for consuming pizza and hamburgers indicates he views them as perfect substitutes, with a utility equation of U(P,H) = P + 4H. Given the prices of pizza at $3 and hamburgers at $6, and a monthly income of $300, he can maximize his utility by purchasing 20 pizzas and 50 hamburgers, achieving a utility of 220. A gift certificate of $60 for pizza allows him to buy 20 pizzas, but the discussion centers on how much cash would provide the same utility without restrictions. The conclusion reached is that the cash amount needed for equivalent utility is less than the gift certificate value. The analysis highlights the importance of understanding utility maximization in consumer choice.
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Homework Statement


Hello. Thats my homework question, so any hints will be appreciated.

Paul consumes only two goods, pizza (P) and hamburgers (H), and considers them to be perfect substitutes, as shown by his utility function: (, ) = + 4. The price of pizza is $3 and the price of hamburgers is $6, and Paul’s monthly income is $300. Knowing that he likes pizza, Paul’s grandmother gives him a birthday gift certificate of $60 redeemable only at Pizza Hut. Though Paul is happy to get this gift, his grandmother did not realize that she could have made him exactly as happy by spending far less than she did. How much would she have needed to give him in cash to make him just as well of as with the gift certificate?

Homework Equations


U(P,H)=P+4H subject to 300\leq 3P+6H

The Attempt at a Solution


Paul can buy 20 pizzas with that gift certificate. I assume that the rest 300$ he will spend on hamburgers which cost 6$, so he will buy 50 hamburgers. When (P,H)=(20,50) the utility he gets is U(20,50)=20+4*50=220. Now, If my reasoning up to this step has been right, I need to figure out another bundle (P,H) which will get as much utility for Paul.
 
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I am no economist, but I strongly suspect that Paul's monthly allowance is irrelevant, and that you just have to concentrate on the utility that grandma's gift might bring if in cash form.
 

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