Can you please help me with this question?

Question

Every day, Dave eats either a sandwich or pizza for lunch. Over 42 days, Dave had pizza 3 times for every 4 times he had a sandwich. Over the next x days, he had pizza 3 times for every 2 times he had a sandwich. If at the end of this entire period he had pizza as many times as he had a sandwich, what is the value of x?

Answer 1

If he had pizza 3 times to every 4 times he had a sandwich in 42 days, then 3 out of every 7 days he had a pizza, which means 18 out of every 42 days he had a pizza (multiplying by 6). This means he had 42-18=24 days he had a sandwich.

Over the next x days he will have pizza 3 times for every 2 times he has a sandwich, which means 3/5 of the days he will have pizza and 2/5 of the days he will have a sandwich.

In total, he will have had 18 + 3/5 x pizzas and 24 + 2/5 x sandwiches. To find x where they will be equal, we equate the two expressions:

18 + 3/5 x = 24 + 2/5 x and 1/5 x = 6, x = 30.

To check after 30 days, he will have 3/5 of 30 = 18 more pizzas and 2/5 of 30 = 12 more sandwiches for a grand total of 36 of each.