Question

working with ratio
ratios can be used in word problems to express the relationship between parts.
example: charlie works as a cook in a restaurant. his chicken soup recipe contains:

• 11 cups of seasoned broth
• 5 cups of diced vegetables
• 3 cups of rice
• 3 cups of chopped chicken

write the ratios for each of the following relationships.
a) vegetables to chicken
b) broth to vegetables
c) chicken to rice
d) chicken to the total ingredients in the recipe
solution: the ratios are the numbers for the items in the order they are asked for.
a) vegetables to chicken is 5:3
b) broth to vegetables is 11:5
c) chicken to rice is 3:3 or 1:1
d) chicken to the total ingredients in the recipe is 3:22 (11 + 5 + 3 + 3)
assignment 3 - working with ratio

1. a conveyor belt has 2 pulleys. one pulley has a diameter of 45 cm and the other has a diameter of 20 cm. what is the ratio of the smaller diameter to the larger diameter?
2. on a bicycle with more than one gear, the ratio between the number of teeth on the front gear and the number of teeth on the back gear determines how easy it is to pedal. if the front gear has 30 teeth and the back gear has 10 teeth, what is the ratio of front teeth to back teeth?
3. what is the ratio of 250 ml of grape juice concentrate to 1 l of water?

(hint: 1000 ml = 1l)

Explanation:

Step1: Identify smaller/larger diameters

Smaller diameter = 20 cm, Larger diameter = 45 cm. Ratio: $20:45$
Simplify by dividing by 5: $\frac{20}{5}:\frac{45}{5}=4:9$

Step2: Identify front/back teeth count

Front teeth = 30, Back teeth = 10. Ratio: $30:10$
Simplify by dividing by 10: $\frac{30}{10}:\frac{10}{10}=3:1$

Step3: Convert units to match

1 L = 1000 mL. Grape juice = 250 mL, Water = 1000 mL. Ratio: $250:1000$
Simplify by dividing by 250: $\frac{250}{250}:\frac{1000}{250}=1:4$

Answer:

1. $4:9$
2. $3:1$
3. $1:4$