Question

Sam and Janet each have a whole number of dollars, and $\frac13$ of Sam's money equals $\frac12$ of Janet's money. Together, they have more than $\$10$. What is the least number of dollars they could have combined?

Answer 1

$15

Explanation:

Let Sam's Money =s

Let Janet's Money =j

`$\frac13$` of Sam's money equals
`$\frac12$` of Janet's money.

Let n be the number of dollars held by Sam and Jane respectively

Therefore:
`$n=\frac13s=\frac12j$`

s=3n

j=2n

s+j=3n+2n=5n

Together, they have more than $10

Therefore:

5n>10

n>2

The least sum they could have is at n=3

At n=3

s+j=5n=5X3=$15

The least number of dollars they could have combined is $15.