We are given
Detective Pi has 5 1/5 quarts of orange juice
we can write in fraction form
we get
![=(5*5+1)/(5)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/bm3gtagq8lpp0jxe21aazn7p8wokmwqyb9.png)
![=(26)/(5)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/y53qjt8u1xf9bxitlpi36igkmae1js2bvv.png)
so,
Detective Pi has
quarts of orange juice
Let's assume
total number of mornings is x
She likes to have 2/5 of a quart every morning
so,
total quantity of juice = total number of morning*She likes to have 2/5 of a quart every morning
total quantity of juice is
![=(2)/(5) x](https://img.qammunity.org/2019/formulas/mathematics/middle-school/b4lz0kocyf4vhahs3l6o8wnusw2vwe3ym6.png)
now, we can set it equal to 26/5
![(26)/(5)=(2)/(5) x](https://img.qammunity.org/2019/formulas/mathematics/middle-school/wcdraz8yxjzum641v90lo86jxwm430vn2h.png)
now, we can solve for x
we can multiply both sides by 5
![(26)/(5)*5=(2)/(5) x*5](https://img.qammunity.org/2019/formulas/mathematics/middle-school/svhcgv816749rpehl8d3z0njmowh9xghx4.png)
![26=2x](https://img.qammunity.org/2019/formulas/mathematics/middle-school/x0u5k4yjxij5zu6zeigvbp65e3w3llr41h.png)
divide both sides by 2
we get
![x=13](https://img.qammunity.org/2019/formulas/mathematics/middle-school/h9stq0a7tl3tgj57bx8thnehintfilur39.png)
so, total number of mornings is 13..........Answer