The Smiths are sending out a batch of holiday cards. Emily signed of the cards. Then Josh signed of the remaining cards. Tatiana signed 20% of what Josh had left. If there were 75 cards in all, how many cards are left to be signed?

Answer: There are 32 cards left to be signed

Step-by-step explanation:

Hi, the correct question is:

The Smiths are sending out a batch of holiday cards. Emily signed 2/5 of the cards. Then Josh signed 1/9 of the remaining cards. Tatiana signed 20% of what Josh had left. If there were 75 cards in all, how many cards are left to be signed?

So, to answer this question:

Emily signed 2/5: so, we have to multiply the number of cards (75) by the amount that she signed:

75 x 2/5 = 30

Then, we subtract the result to the total amount of cards:

75-30 = 45 cards left to be signed

Repeating the process with Josh (now the total number of cards is 45)

45x 1/9 = 5 45-5 = 40

And finally we repeat the process with Tatiana (using the decimal form of 20% ⇒ 20/100 = 0.2)

40x 0.2=8 40-8 = 32 cards left to be signed

Step-by-step explanation:

Let x be the number of cards

Given:

Emily = 2/5 of x

Josh, Tj = 1/9 * (1 - 2/5 * x)

Tatiana = 20/100 * (1 - Tj)

Therefore, x = 75

Emily signed = 2/5 * 75

= 30

Card left unsigned = 75 - 30

= 45

Josh signed = 1/9 * 45

= 5

Card left unsigned = 45 - 5

= 40

Tatiana signed = 1/5 * 40

= 8

Card left unsigned = 40 - 8

= 32

Cards not signed = 32