Model Method - Questions and Answers



Question posted by Yarn Xee from Singapore:

Grade/Level: Primary 6

Question: Karen is about as many days as her mother is in weeks and Karen is as many months as her grandpa is in years. Karen, her mother and her grandpa are 160 years old altogether. How old is her grandpa?

Answer:

Step 1: It is easier to solve this question with the ratio method. Since Karen is about as many days as her mother is in weeks,

Karen : Mother

= 1 day : 1 week

= 1 day : 7 days

Step 2: Since the relationship between Karen and the grandpa is expressed in terms of months and years, we need to convert that to days for ease of comparison among the 3 people,

Karen : Grandpa

= 1 month : 1 year

= 1 month : 12 months

= 4 weeks : 48 weeks

= 28 days : 336 days


Please note that we have taken the following assumptions as the question is unclear (usually such assumptions will be stated in the question):

1 week = 7 days

1 month = 4 weeks = 28 days

1 year = 12 months = 48 weeks = 336 days


Step 3: Combining step 1 and 2,

Karen : Mother

= 1 day : 7 days

= 28 days : 196 days

Karen : Mother : Grandpa

= 28 days : 196 days : 336 days

= 28 units : 196 units : 336 units

28 units + 196 units + 336 units = 560 units

Since the total of their ages is 160 years,

560 units ------------> 160 years

1 unit ------------> 160 years / 560 = 2/7 years

336 units ------------> 2/7 years X 336 = 96 years

Therefore, her grandpa is 96 years old.