Question

Maddy and Lara see a list of numbers written on a blackboard. Maddy adds $3$ to each number in the list and finds that the sum of her new numbers is $45.$ Lara multiplies each number in the list by $3$ and finds that the sum of her new numbers is also $45.$ How many numbers are written on the blackboard?

$10$

$5$

$6$

$8$

$9$

Answer: A

Concepts:system of equations summation

Difficulty rating: 1130

Solution:

Let $S$ be the original sum and $n$ the number of entries. Maddy adds $3$ to each, so her total is $S + 3n = 45.$ Lara triples each, so hers is $3S = 45,$ giving $S = 15.$ Then $15 + 3n = 45,$ so $n = 10.$ Thus, A is the correct answer.

2023 AMC 10B Problem 5

Answer: A

Difficulty rating: 1130

Solution:

Problem 5 in Other Years