A beverage stall has 70 bottles of orange juice and 48 bottles of mango juice. Every day the stall uses 5 bottles of orange juice and 3 bottles of mango juice. After how many days, the remainder bottles of both juices are the same? And find the number of remainder bottles.
70 - 5 d = 48 - 3 d
2 d = 22
d = 11
70 - 5 d = 70 - 55 = 15
48 - 3 d = 48 - 33 = 15 luckily
To find the number of days it takes for the remainder bottles of orange juice and mango juice to be the same, we can set up an equation. Let's denote the number of days as "d", the initial number of orange juice bottles as "O", the initial number of mango juice bottles as "M", and the number of bottles used daily as "UO" for the orange juice and "UM" for the mango juice.
Given:
O = 70 (initial number of orange juice bottles)
M = 48 (initial number of mango juice bottles)
UO = 5 (number of orange juice bottles used daily)
UM = 3 (number of mango juice bottles used daily)
We can calculate the remainder bottles for each juice after "d" days using the formula:
Remainder = Initial number - (Number used daily × Number of days)
For the orange juice, the remainder after "d" days is:
RO = O - (UO × d)
For the mango juice, the remainder after "d" days is:
RM = M - (UM × d)
To find the number of days required for the remainder bottles of both juices to be the same, we need to set RO equal to RM and solve for "d":
RO = RM
O - (UO × d) = M - (UM × d)
Substituting the given values:
70 - (5 × d) = 48 - (3 × d)
Now, let's solve for "d":
70 - 5d = 48 - 3d
(70 - 48) = 5d - 3d
22 = 2d
d = 11
Therefore, it will take 11 days for the remainder bottles of orange juice and mango juice to be the same.
To find the number of remainder bottles after 11 days, we can substitute the value of "d" back into the equations for RO and RM:
RO = O - (UO × d)
RO = 70 - (5 × 11)
RO = 70 - 55
RO = 15
RM = M - (UM × d)
RM = 48 - (3 × 11)
RM = 48 - 33
RM = 15
Hence, after 11 days, there will be 15 remainder bottles of both orange juice and mango juice.