30% of the rabbits from a farm were lent to a zoo. After a month, 5/6 of the rabbits were returned to the farm. There were 228 rabbits in the farm now.
a.) How many rabbits were lent to the zoo in the beginning?
b.) How many rabbits were there at the farm before they were lent to the zoo?
What answer did you come up with?
213
why in this site is hard to find the answer
5/6=0.83
1-0.83=0.17
228/0.17=1342 rabbits
1342×0.83=1114 rabbits returned to farm
1342÷0.3=4474 total number of rabbits at the first.
x = total rabbits in farm
y = rabbits lent to zoo
0.3 x = y - - > EQ. 1 (30% of rabbits from a farm lent to zoo)
5/6 y + 0.7 x = 228 - -> EQ. 2 (5/6 of lent rabbits were returned added to what was left of 30%)
Substitute EQ1 to EQ 2
(5/6) 0.3x + 0.7 x = 228
0.25 x + 0.7 x = 228
0.95 x = 228
x = 228 / 0.95
x = 240 total rabbits in farm
y = 0.3 x
y = 0.3 (240)
y = 72 rabbits lent to zoo
a)72
b)240
To find the answers to both questions, we can follow these steps:
Let's assume the total number of rabbits lent to the zoo initially is "x".
a) We know that 30% of the rabbits from the farm were lent to the zoo, so we can set up an equation:
30% of the total number of rabbits = x
0.30 * Total number of rabbits = x
To find the total number of rabbits, we can use the information given in the problem. After a month, 5/6 of the rabbits were returned to the farm, which means there were (1 - 5/6) = 1/6 of the rabbits left at the zoo.
0.30 * Total number of rabbits * (1/6) = x
Now we can solve this equation to find the value of x.
0.30 * Total number of rabbits * (1/6) = x
(1/6) * Total number of rabbits = x
Since we know x is equal to 228 (the number of rabbits currently on the farm), we can substitute:
(1/6) * Total number of rabbits = 228
Now we can solve for the total number of rabbits:
Total number of rabbits = 228 * 6
Total number of rabbits = 1368
b) To find the number of rabbits on the farm before they were lent to the zoo, we can subtract the number of rabbits lent to the zoo from the total number of rabbits initially:
Number of rabbits on the farm = Total number of rabbits - Number of rabbits lent to the zoo
Number of rabbits on the farm = 1368 - 228
Number of rabbits on the farm = 1140
Therefore, the initial number of rabbits lent to the zoo was 228, and the number of rabbits on the farm before they were lent to the zoo was 1140.