Answer: Let's call the ages of the squirrels C, Celia, and Cecily, and let's represent the number of nuts they took with the variables c, ce, and ce2, respectively.
We know that the total number of nuts is 770, so we can write:
c + ce + ce2 = 770
We also know the ratios of the nuts each squirrel took relative to the others:
Cedric takes 3 nuts for every 4 nuts Celia takes, so we can write c : ce = 3 : 4, or c = (3/4)ce.
Cecily takes 7 nuts for every 6 nuts Celia takes, so we can write ce2 : ce = 7 : 6, or ce2 = (7/6)ce.
Now we can substitute these expressions into the first equation and solve for ce, the number of nuts Celia took:
(3/4)ce + ce + (7/6)ce = 770
Multiplying both sides by 12 to eliminate the fractions, we get:
9ce + 12ce + 14ce = 9240
Simplifying, we get:
35ce = 9240
Dividing both sides by 35, we get:
ce = 264
Now that we know Celia took 264 nuts, we can use the ratios to find how many nuts the other squirrels took:
Cedric took 3/4 as many nuts as Celia, so he took (3/4) * 264 = 198 nuts.
Cecily took 7/6 as many nuts as Celia, so she took (7/6) * 264 = 308 nuts.
Finally, to find how many nuts the youngest squirrel took, we can subtract the nuts taken by the other two squirrels from the total:
c + ce2 = 770 - ce
c + ce2 = 770 - 264 - 198 - 308
c + ce2 = 0
This means that the youngest squirrel did not take any nuts.
Explanation: