Question

AMMA

Richard owned n cows
Ellis had exactly 4 times as many cows as Richard,
Richard buys 13 extra cows.
Ellis sells 9 of his cows
Ellis still has more cows than Richard
Form an inequality, in terms of n
Solve the inequality to find the least value of n
You must show all your working

Answer 1

n ≥ 8

Explanation:

Let R and E stand for the number of cows owned by Richard and Ellis, respectively.

We are told that:

R = n

E = 4n

Then:

R = n+13 [Bought 13 cows]

and

E = 4n-9 [Sold 9 cows]

Still:

E > R [Ellis still has more cows]

Therefore:

4n-9 > n+13

3n > 22

n > 7 1/3

Since no rancher wants 1/3 of a cow, we need to round either up or down to a whole number. The least value of n is therefore 8 cows or higher. Since 8 is a valid number, change the > inequality to ≥.

n ≥ 8