Question

Joan waters her plants each day with 25 1/2 gallons of water. with a new irrigation in place, she uses 19 3/4 gallons of water each day. how many gallons of water does she save in a 30-day period with the irrigation system?

Answer 1

she waters her plants with 25 1/2 gallons
with the new system, she does it with 19 3/4, what's the difference/savings?


`\bf \begin{cases} 25(1)/(2)\implies \cfrac{25\cdot 2+1}{2}\implies \cfrac{51}{2} \\\\\\ 19(3)/(4)\implies \cfrac{19\cdot 4+3}{4}\implies \cfrac{79}{4} \end{cases} \\\\\\ \cfrac{51}{2}-\cfrac{79}{4}\implies \cfrac{102-79}{4}\implies \cfrac{23}{4}\ gallons\ per\ day\impliedby \textit{LCD of 4} \\\\\\ \textit{now, how much will it be for 30days?}\qquad 30\cdot \cfrac{23}{4}\implies \cfrac{15\cdot 23}{2} \\\\\\ \cfrac{345}{2}\implies 172(1)/(2)\textit{ gallons}`