1. Iva and Maja received an order to make 72 greeting cards. Each of them made 36 cards, and each of their cards took the same amount of time to make. Iva made 6 cards in the same time it took Maja to make 5 cards. Iva finished making her 36 cards 1 hour and 48 minutes before Maja finished all of hers. How many cards did Iva and Maja each make in 1 hour?
First solution.

Let $x$ be the time it took for Iva to make 6 cards, and for Maja to make 5 cards.

Then, it took Iva $\frac{x}{6}$ hours to make one card, and Maja $\frac{x}{5}$ hours.

This means that Iva made her 36 cards in $\frac{36}{6} x=6 x$ hours, and Maja in $\frac{36}{5} x$ hours.

Convert 1 hour and 48 minutes to hours.

1 minute $=\frac{1}{60}$ hours.

$\Rightarrow$ 1 hour and 48 minutes $=\frac{108}{60}=\frac{9}{5}$ hours.

1 POINT

Since it took Iva 1 hour and 48 minutes less time to make the cards than Maja, the equation holds:

$6 x+\frac{9}{5}=\frac{36}{5} x$

3 POINTS

$30 x+9=36 x$

1 POINT

$6 x=9$

$x=\frac{9}{6}=\frac{3}{2}=1 \frac{1}{2}$

1 POINT

Iva makes 6 cards in 1 hour and 30 minutes, which means she makes 6: $1 \frac{1}{2}=4$ cards in 1 hour.

1 POINT

Maja makes 5 cards in 1 hour and 30 minutes, which means she makes

$5: 1 \frac{1}{2}=3 \frac{1}{3}$ cards in 1 hour.

1 POINT

TOTAL 10 POINTS