At first, Nathan had $92 and Mabel had $50. Each of them bought a book at the same price. The ratio of the amount of money Nathan and Mabel had left was 5 : 2. How much did the book cost? Ans: ___

1. Find the difference in the amount of money Nathan and Mabel had at first.

Difference $= 92 - 50 = 42$

2. Relate the constant difference to the ratio of the amount left.

Since they spent the same amount on the book, the difference in the amount they had left remains the same.
Difference in ratio units $= 5 - 2 = 3 \text{ units}$
$3 \text{ units} = \char36{}42$

3. Find the amount Mabel had left and calculate the cost of the book.

$1 \text{ unit} = 42 \div 3 = 14$
Mabel's amount left $= 2 \text{ units} = 2 \times 14 = \char36{}28$
Cost of the book $= 50 - 28 = \char36{}22$