In what number base is the addition 465 + 24 + 225 = 1050?

To solve this problem, we need to find out in what base the addition statement is true. Let's assume the base is "b". Then, in the units column, we have: - 5 + 4 = 10, so we write down 0 and carry-over 1. - In the "b" column, we have: 6 + 2 + 2 + 1 = 11, so we write down 1 and carry-over 1. - In the "b^2" column, we have: 4 + 2 + 5 + 1 = 12, so we write down 2 and carry-over 1. - In the "b^3" column, we have: 4 + 2 + 2 = 8. Putting these digits together, we get the number 8201 in base "b". Now, we need to check if this number is equal to 1050 in base 10. 8201 in base "b" means: 8 x b^3 + 2 x b^2 + 0 x b + 1 x 1 = 1050 Rearranging the terms, we get: 8 b^3 + 2 b^2 + 1 = 1050 Subtracting 1 from both sides: 8 b^3 + 2 b^2 = 1049 Since b is a positive integer, we can see that b must be greater than 5. Trying b = 6, we get: 8 x 6^3 + 2 x 6^2 = 1048 This is not equal to 1049, so we need to try a larger base. Trying b = 7, we get: 8 x 7^3 + 2 x 7^2 = 1049 This is equal to 1049, so the base is 7. Therefore, the answer is seven.