Question

Noah is learning portugese, and he uses flash cards to study vocabulary. For every 5 new flash cards he practices, he reviews 10 old flash cards. Today , he practiced 45 flash cards in all. How many new flash cards did he practice?

Answer 1

Answer:  15

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Explanation:

n = number of new flash cards practiced

2n = number of old flash cards practiced

The 2n is due to the fact that the number of old flash cards is double that of the new ones (eg: 10 is twice that of 5).

The two expressions must add to 45.

new + old = total

n + 2n = 45

3n = 45

n = 45/3

n = 15

2n = 2*15 = 30

Noah practiced 15 new flash cards and 30 old flashcards which is a total of 15+30 = 45. This confirms our answer.

Also note that the ratio of new to old is 15:30 which reduces to 1:2, then we can multiply both sides by 5 to get 5:10. This effectively shows that 15:30 and 5:10 are the same equivalent ratio (just in different forms). This helps confirm our answer.