# Find number of policies sold.An insurance agent gets a base salary of $250 per week, he also gets an extra $2 per policy if the number of policies sold is more than 10 and an extra $1 per policy if...

Find number of policies sold.

An insurance agent gets a base salary of $250 per week, he also gets an extra $2 per policy if the number of policies sold is more than 10 and an extra $1 per policy if the number of policies sold is more than 50. How any policies did he sell if he earned $450?

*print*Print*list*Cite

We are given the base pay is 250. Now out of the total amount earned, 250 was the base pay. Therefore the commission was (450 – 250). Now let’s say the number of policies sold is N. For the first fifty policies, he earns $2 per policy staring from the 11th. Therefore he earns 40*2 = 80. For the rest of the policies he gets $3 per policy. Therefore for N-50 he gets $3 per policy

Now total income is 250 + 80 + (N-50)*3 = 450

=> 250 + 80 + 3N – 150 = 450

=> 3N = 270

=> N = 270/ 3

=> N = 90

**Therefore he sold 90 policies.**

Out of $450 the agent earned , $250 is his base salary.

So the extra herned is $(450-250) = $200.

Therefore the extra $200 is due to the earning of selling more than 10 policies or more than 50 policies.

So selling more than 10 up to 50 policies the earning he gets = (50-10)*2 = 80 dolars.

But he earned 200 dollars extra.

So he has earned $(200-80) = $120 on account selling more than 50 polies. If he sells more than 50 policies, he earns 3 dollars , ona ccount of exceeding both 10 and 50 limits.

So the number of policies above he should sell to the extra $120 = 120/3 = 40.

Thereforee in all he should sell 50+40 = 90 policies to earn $450.

The components of earnings:

Base earnung = $250

Extra eanings for 90 policies:

First 10 : nill

11 to 50: 40*2 = $80

51 to 90 : 40*3 = $120