Find three consecutive numbers?

Consecutive numbers are whole numbers that follow in order such as 7, 8, 9, 10, 11, and 12. Find three consecutive numbers such that the sum of first and third is 118.

For three consecutive numbers the average of three will be the middle number given by sum of the numbers divided by 2.

i.e; 118/2 will be the middle number which is equal to 59.

The three consecutive numbers are 58, 59 and 60.

What is the average of the six weights?

The average of five weights is 13 grams.This set of five weights is then increased by another weight of 7 grams. What is the average of the six weights?

Average Weight = \(\dfrac{Total Wt}{5}\) = 13
Total Weight = 13 * 5 = 65
When another weight of 7 grams added Total weight = 65+7 = 72

Average Weight = \(\dfrac{72}{6}\) = 12

Average of six weights is 12 gms.

Average speed for the entire trip?

A motorist made a 60 mile trip averaging 20 miles per hour. On the return trip, he averaged 30 miles per hour. What is the motorist's average speed for the entire trip?

Average speed = Total distance travelled / Total time taken

Total distance for the trip = 60+60=120 miles
Total time taken for the trip = 60/20+60/30=3+2=5 hours.

So the average speed = 120/5=24 mph.

Motorist's average speed for the entire trip is 24 miles per hour.

Average score for all four bowling games?

In three bowling games, Alice scores 139, 143 and 144. What score will Alice need in a fourth game in order to have an average score of 145 for all four games?

MetroEye: Average Score = Sum of scores / Number of games

i.e; 145 = (139+143+144+S)/4
426+S = 145×4
S = 154

Hence Alice will need a score of 154 in the fourth game.

Average weight of a group of children

The average weight of a group of children is 100 pounds. Todd, who weighs 112 pounds, then joins the group. This raises the average weight of the group to 102 pounds. How many children were there in the original group?

Let N be the number of children in the group. W be the total weight of children.

=> Average weight = W/N = 100 i.e; W = 100N

When Todd is added to the group, average weight is 102 pounds.
=>(W+112)/(N+1)=102

Substituting for W;
100N+112=102(N+1)
100N+112=102N+102
=>2N=10
=>N=5

There were 5 children in the original group.