Sarah's age - Math Central

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Question from Kenneth:

Hello:

2/3 of Mary's age equals Sarah's age and 3/4 of Ruth's age equals Sarah's age.
If the total ages equal 46, how old is each girl?

Answer: Mary 18, Ruth 16, Sarah 12

Solution:

3/2 of Sarah's age equals Mary's age.
4/3 of Sarah's age equals Ruth's age.
6/6 of Sarah's age equals Sarah's age.

46 divided by 23/6 equals Sarah's age of 12.

Can the following similar situation be solved if the two girls ages do not equal Sarah's age?

2/3 of Mary's age equals Ruth's age and 3/4 of Ruth's age equals Sarah's age. How old is each girl?

Their ages may not be the same as those in the above example.

I thank you for your reply.

Kenneth,

"2/3 of Mary’s age equals Ruth’s age'': You multiply by 3/4:
"3/4 x (2/3 of Mary’s age) equals 3/4 x (Ruth’s age)''.
Then use 3/4 x 2/3 = 1/2, and 3/4 x Ruth's age = Sarah's age:
"1/2 of Mary’s age equals Sarah’s age''.

Claude

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