Question

A toy company manufactures games. They sell 4 board games in a box. They sell 10 decks of playing cards in a box. Mrs.

Johnson wants to buy an equal number of board games and decks of playing cards for the Boys and Girls Club
Part A
What is the least number of board games she can buy?
The least number of board games Mrs. Johnson can by is
Part B
How many boxes of decks of playing cards should Mrs. Johnson buy if she wants the least number of board games and
decks of playing cards?
boxes of decks of playing cards if she wants to least number of
Mrs. Johnson should buy board games and decks of playing cards.

Answer 1

• Mrs. Johnson should buy 5 boxes of board games to get 20 board games.
• 2 boxes of decks of playing cards to get 20 decks, ensuring she has an equal amount of both.

Step-by-step explanation:

For Part A

To find the least number of board games Mrs. Johnson can buy, we must find the smallest common multiple of 4 and 10 since board games are sold in boxes of 4 and decks of playing cards in boxes of 10. The least common multiple (LCM) of 4 and 10 is 20.

Therefore, Mrs. Johnson can buy 5 boxes of board games to have 20 board games.

For Part B

Since Mrs. Johnson is buying 20 board games, which is 5 boxes of 4 games each (20 / 4 = 5), she will need to purchase 2 boxes of playing cards since each box contains 10 decks of cards (20 / 10 = 2).

The least number of board games Mrs. Johnson can buy is 20, and she should buy 2 boxes of decks of playing cards to match the number of board games.