1. The problem involves writing and understanding ratios between quantities such as cups of cereal and cups of pecans, balloons blown up by Leo and Kathy, and tickets sold by classes. 2. To write the ratio of cups of cereal to cups of pecans, you can express it in three ways: as a fraction, with a colon, or in words. For example, if cereal is $c$ cups and pecans is $p$ cups, the ratio can be written as: $$\frac{c}{p},\quad c:p,\quad \text{or } c \text{ to } p$$ 3. The ratio of cereal to pecans compares part to part because it compares one part (cereal) directly to another part (pecans). 4. The total amount of snack mix is the sum of the cups of cereal and cups of pecans: $$\text{Total} = c + p$$ 5. Ratios comparing each ingredient to the total snack mix are: $$\frac{c}{c+p},\quad \frac{p}{c+p}$$ 6. To write a ratio comparing two different quantities, express the quantities as a fraction, with a colon, or in words, always keeping the order consistent to show which quantity is compared to which. 7. For Leo and Kathy's balloons: - Ratio of Kathy's balloons to Leo's balloons: $$\frac{5}{7},\quad 5:7$$ - Ratio of Leo's balloons to Kathy's balloons: $$\frac{7}{5},\quad 7:5$$ - Ratio of total balloons to Leo's balloons: Total balloons = $7 + 5 = 12$ $$\frac{12}{7},\quad 12:7$$ 8. For ticket sales: - Ratio of Miss Garcia's sales to the goal: $$\frac{87}{100},\quad 87:100$$ - Ratio of Mr. Carpenter's sales to the goal: $$\frac{113}{100},\quad 113:100$$ - Ratio of Mr. Carpenter's sales to Miss Garcia's sales: $$\frac{113}{87},\quad 113:87$$