Increase or decrease? – Solution

This is the solution to the monthly maths problem from RTSdécouverte Increase or decrease?

**Solution:**

The number of unemployed slightly increased (by around 0.67%) in the 10 years while the price of coffee fell (by 9%) over 30 years.

Concerning the number of unemployed, let P be the number of people in the workforce at the time of the first measurement. This number increased by 20% over the 10 years, so after 10 years it is

P + 20/100 ∙ P = 120/100 P = 1.2 P

The number of unemployed initially was 9% of the workforce, that is 9/100 ∙ P = 0.09 P.

10 year later 8% of the workforce were unemployed making 0.08 ∙ (1.2 P) = 0.096 P.

As 0.096 P > 0.09 P the (absolute) number of unemployed increased.

Concerning the price of coffee, let C be the initial price. After the first increase the price becomes

C + 30/100 ∙ C = (1 + 30/100) ∙ C = 1.3 C

After the second increase the new price is

1.3 C - 50/100 ∙ (1.3 C) = 0.5 ∙ (1.3 C)

Similarly, after the next price increase the new price is

1.4 ∙ 0.5 ∙ (1.3 C) = 0.91 C

This means a 9% reduction in the purchase price of coffee on production.

You can read the original problem here: Increase or decrease?

Original RTS Problèmes du mois (FR)