Question 30. Ava writes a 3-digit number on the whiteboard. Then Brandon writes a 4th digit to the right of the previous ones. He says, look, the number increased by 2024. What digit did Brandon write? First, we can represent the 3-digit number Ava wrote as ABC, and we can represent the 4th digit Brandon added as D. Notice how when we multiply ABC by 10, we end up with a number in the form of ABC zero. Then if we add a D to it, we get ABCD. Therefore, ABCD is equal to ABC times 10 plus D. Now let's look at the second half of the question. Brandon says, look, the number increased by 2024. Therefore, the difference between ABCD and ABC is 2024. Since we know that ABCD is equal to ABC times 10 plus D, we can write that instead of ABCD, giving us ABC times 10 plus D minus ABC equals 2024. We can simplify this further by combining the ABCs. 10 ABC minus 1 ABC is 9 ABC. And we're left with ABC times 9 plus D equals 2024. Notice how this equation we're left with looks very similar to division with remainders, with 2024 being the dividend, 9 being the divisor, ABC being the quotient, and D being the remainder. We can solve the equation 2024 divided by 9 to get ABC and D. We get that abc equals 224 and d equals 8, which means that Anna wrote the number 224 and Brandon wrote the digit 8, creating 2248. Subtracting 224 from 2248 results in 2024, which means that adding the 8 at the end really did increase the number by 2024. Since Brandon wrote the digit 8, our answer will be d.

number puzzle

equation solving

digit addition

math problem

number increase