My last brain cell isn't cooperating. a) on a trip to a lake, kerrie and shelly rode their bicycles four more than three times as many miles in the afternoon as in the morning. if the entire trip was 112 miles long, how far did they ride in the morning and how far in the afternoon. b) mr. and mrs. patton and their daughter, carolyn, own three cars. carolyn drives 10 miles per week farther in her car than her father does in his. mr, patton drived twice as many miles per week as mrs. patton. if their total mileage per week is 160 miles, how many miles per week does each of them drive? c) 10,483 people attended a rock festival. if there were 811 more boys than girls, and 2,481 fewer adults over 50 years of age than there were girls, how many of each group attended the festival?

A) 27, 85

B) 70, 60, 30

C)  B=43,750, G=42,940, A=18,130

The difference is that we have to square both sides 'n' number of times in order to eliminate the radical in solving the radical equation with 'n' number of radicals.

We know that a radical equation is an equation involving square root and other roots.

When we solve a radical equation, we isolate the radical part and then take square of both sides to solve for the unknown variable.

1. Equation with one radical.

Let us consider,

Squaring on both sides,

i.e.

i.e.

i.e.

2. Equation with two radicals.

Let us consider, .

i.e. ( Squaring both sides )

i.e.

i.e.

i.e.  ( Squaring both sides )

i.e.

i.e.

i.e.

i.e.

So, we can see that the method for solving both 1 and 2 is same, the only difference is that in 2 we have to square both sides two times in order to eliminate the radical.

Hence, the difference is that we have to square both sides 'n' number of times in order to eliminate the radical in solving the radical equation with 'n' number of radicals.