2023 AMC 10B Problem 5

Problem 5 of 25EasierAlgebra

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?

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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,

n = 10.

Thus, A is the correct answer.