Question

One store got $1.2$ times as much apple cider as the second store.

Every hour the first store was selling $90$ liters of cider, while the second one was selling $80$ liters per hour.

In $2.5$ hours the second store had $65$ liters less than the first store.

How many liters of cider were delivered to each store $?$

Answer 1

Find the volume of liters of cider sold to each store:

Let the second store got $x$ liters.

Then, the first store got $1.2x$ liters.

Volume of cider sold by first store in $1$ hour $=$$90$ liters.

Volume of cider sold by first store in $2.5$ hour $=$$90\times 2.5$

$=225$ liters.

So the volume of cider left in first store $=$ $(1.2x-225)$ liters

Volume of cider sold by second store in $1$ hour $=$ $80$ liters.

Volume of cider sold by second store in $2.5$ hour $=80\times 2.5$

$=200$ liters.

So the volume of cider left in second store $=$ $(x-200)$ liters

Now, find the difference in volume of cider sold by two stores as follows:

$=(1.2x-225)-(x-200)$

$=1.2x-225-x+200$

$=0.2x-25$

Since the difference in volume of cider left is $65$:

$65=0.2x-25$

$\Rightarrow$ $90=0.2x$

$\therefore$ $x=450$ liters

$1.2x$.$=1.2\times 450$

$=540$ liters

Hence, cider delivered to the first store is $\mathbf{540}\mathbf{}\mathbf{\text{liters}}$ and to the second store is $\mathbf{450}\mathbf{}\mathbf{\text{liters}}$.