7.3. Yesterday, Sasha cooked soup and put in too little salt, so he had to add more salt. Today, he put in twice as much salt, but still had to add more salt, though only half the amount he added yesterday. By what factor does Sasha need to increase today's portion of salt so that he doesn't have to add more salt tomorrow? (Each day Sasha cooks the same portion of soup.)
Answer: 1.5 times.

Solution. We will present two methods of solving: "arithmetic" and "algebraic."

First method. Doubling the amount of salt compensated for half of yesterday's addition, so the initial amount of salt that Sasha put in yesterday is one-third of the required amount. Therefore, the initial amount of salt that Sasha put in today is two-thirds of the required amount. Consequently, tomorrow he needs to add one and a half times more.

Second method. Let Sasha put $x$ g of salt in the soup yesterday, and added $y$ g. Then today he put $2x$ g, and added $-0.5y$ g. According to the condition: $x + y = 2x + 0.5y$, so $x = 0.5y$. Thus, the total amount of salt required is
$2x + 0.5y = 3x$ g, and today Sasha put $2x$ g. Therefore, today's portion of salt needs to be increased by $3x : 2x = 1.5$ times.

## Grading criteria:

+ correct answer and correct solution with full justification

$\pm$ correct reasoning with full justification, but the answer is given to a different question

$\mp$ correct answer and verified that it satisfies the condition, but not justified that it is the only one

干 correct answer obtained by considering specific numerical values

- only the answer is provided